You want f/2.8 if you can get it, but f/4 is perfectly fine for sports. Some of the longer lenses (like 500mm and up) don’t come in anything less than f/4. Plus there’s a pretty cool 200-400mm f/4 zoom which has become quite popular in professional sports photography. Still, other than the super-telephotos, you do generally want something f/2.8 (or faster, although you’ll probably not be shooting sports more open than f/2.8)
Get her a copy of Understanding Exposure for a gift - it’s really good for people learning how to take photographs instead of snapshots.
I use Canon, and I can offer some advice. Canon lenses, particularly the “L” series are excellent. They do take better pictures. However, it is the photographer that is the biggest factor in good photos. I can tell you this because I have the best lenses and years of experience, but I take mediocre pictures most of the time.
My advice to your wife would be to start carrying her camera with her everywhere, take thousands of pictures, study composition. Then if she still is interested, spring for the “L” lens. After talent, the lens is the most important factor in a great picture. I changes me from poor photographer to passable photographer.
The kit lens is fine to find out if you want to be an amateur.
This, because there are so many different ways that a photo can turn out better or worse because of the lens. Some of them can be mitigated by how the photographer uses the lens, and some can be helped by buying a better lens.
For instance, when first I bought my DSLR, I ended up buying the relatively low-end kit lens along with the best prime lens that money can buy for this lens mount. I got sharp and not very sharp photos out of both of them at first, which puzzled me, so I put some work into figuring out what was going on. In my case, it was because I wasn’t paying attention to how the sharpness of the lenses depended on the aperture-- depth of field aside, lenses also have different degrees of sharpness at different apertures (and, for zoom lenses, at different focal lengths), and the aperture for the maximum center and edge sharpness can be different, too. Once I realized that, I started taking much better pictures with both the kit lens and the fancy prime lens.
YMMV, but once you’ve exhausted all of your options for improving the image quality without getting a new lens, then it’s time for a new lens.
Here are photos taken on freakin’ iPhones, fer cryin’ out loud. Equipment is not nearly as limiting as the nut behind the lens 
Also get her the 50mm 1.8 if you can afford $100. Those two together will be more valuable than a new zoom lens for someone who wants to learn.
I have two colleagues who do extensive iPhone photography. One of my favorite is Steve Serio, who works for Crain’s here in Chicago, and has this great Instagram feed of iPhone photos. He even had one assignment in Crain’s he shot fully on an iPhone that was published.
Another colleague, Mark Hirsch, published a rather intriguing book called That Tree where he basically documented (and still documents) one particular bur oak tree near his home in Dubuque, Iowa. It’s rather amazing what an iPhone can do and how well you can actually print to something like 12"x12" or so. I can certainly tell it’s not a dSLR, but from normal viewing distances, it’s not at all evident to a non-photo geek. Impressive stuff, really.
My nephew Rick is a photographer. He takes better photos with disposable cameras than I can take with really flash gear.
A friend, who had come in to a lot of money and wanted to get serious about photography, asked me to ask Rick for advice on what camera to buy. Rick’s advice was buy any camera you like with a 35mm fixed focal length lens, spend the rest of the money on lessons in graphic design and learn to use one tool properly. He said if my friend did that for a couple of years and needed more advice he would happily provide it then.
Do you really need IS for landscape photography?
Generally you’re not using a lot of zoom, have a lot of light, and since depth of field isn’t an issue you can open up the aperture to get an even faster shutter speed. That mountain isn’t going to go anywhere, so you can take time to brace yourself, or even set up a tripod if you have one.
If I had a DSLR with a cheap kit lens I’d get a 50mm prime lens before before anything else so I could get sharp pictures on the majority of shots that don’t require a zoom.
I would like to ‘third’ this idea. I had the 50mm 1.4 and I loved it. Then my camera fell out of my backback when I was unloading it from the truck and it broke the lens. I was very sad. I replaced it with the 50mm 1.8 at 1/4 of the price.
My pictures improved quite a bit with both lenses because I would put the fixed-length lens on and go for long walks. Without the ‘crutch’ of the kit zoom lens, I found myself thinking a lot more about lighting and depth of field and composition. The extra light gathering capability of the 1.8 gives you a lot more options.
The other thing I did that improved my outdoor photos was to get a polar filter. I got a lot of bang for my bucks out of that.
On the subject of a single fixed focal length lens - I used to use a medium wide (about 35mm 35mm equivalent format). And my second favourite lens was a super wide (21mm 35mm format equivalent.) For travel and landscape these were great. You can always get closer to many things, but you can’t usually get further away. Of course there are always tradeoffs, but the wides were wonderful. I trekked around the planet a couple of times with one of these. It took stunning pictures. Yet it is hard to get a simpler camera.
A little bit of reading can go a long way. The first camera book I read was one in the shop - I didn’t buy it but learnt a lot in those 30 minutes. There are some basics which can make/break a shot. I find the light a serious contributor to how a landscape turns out, when using a basic camera. It can make a huge difference when taking landscape pictures, so much so that if I lose the light I won’t bother framing because, apart from recording the memory, the shot isn’t going to be worth the post-production time and it isn’t going to be something I want to show friends. Bad light can be too bright or too dark. Depending on the camera the optimum level is somewhere between those two. Sunset and sunrise often will be excellent times for taking landscape photographs.
Balance is the other variable you can control on the cheapest of cameras. I mean balancing the objects in view; using the rule of thirds, trying not to overwhelm the picture with stimuli, recording the feelings you’re having - in landscape photography I see abundance, bleakness, beauty, freshness, dark moods, rejuvenation, continuity, nature. I take a lot of photos just as aids to my memory (which isn’t that hot) but I put the good ones on social media and photography websites; the ones on social media get a lot of positive feedback, which is nice. I know they’re not very good, I see stuff online every day which is much better, but I have thousands I’ll be able to look at in the future, if I want, and they’ll bring back some nice memories.
I’m not a serious photographer, at all. I just got a Fuji S8200 and have had an F200EXR for a few years. They’re okay for snapping, posting online, recording moments, but in no way will they ever be suitable for professionals. You can buy lenses and bodies worth thousands but what’s the point if it’s just a hobby? Yes, I’d love a $20k kit, but I’d also love to have a Ferrari. Neither is going to happen, unless I rent them, and I wouldn’t know what to do when travelling around with $20k of camera hanging under my arm.
And kudos to the dedicated photographers posting here. Maybe in a few years I’ll have enough knowledge and skill to be able to talk in the same language (f stop, focal length) and give as good advice. Every time I read about photography I learn something.
…bah humbug. I hated the 50mm 1.8. Worst lens I ever bought and the only photography purchase I actually regretted. It is indeed an affordable good option for a beginner. But try it first before you buy it if you can.
Off-the-duff:
Lens: 40%
Film 30%
Photographer: 30%
When you can intelligently discuss the other two AT LENGTH, we can discuss lens.
It is a poor workman who blames his tools - to a point.
In 35mm format:
20-30 - landscape
30-50 (mostly vertical) buildings
85-150 - portrait (learn “fill flash”) and table-top product
Over 150 - wildlife which might consider you lunch.
I used a cheapie zoom and a good zoom for the same shot - I don’t need to look at the nortes to tell which is which
The Canon 50mm f/1.8 is not the most rigidly constructed lens, and does feel a bit (to put it mildly) plasticky. The optics on it, though, are amazingly good for the price. Bang-for-buck, it’s hard to go wrong with it. Worst case scenario, you’re out a hundred bucks. The only complaint I can see about it is the focal length not being conducive to what you want to shoot, or you having a higher budget that you can spend on better lenses.
I’m a bit late to this party, but anyway…
I’m a Canon CPS member, which means I’m supposed to know something about this.
I’d stick with the kit lens for a while, at least to make sure that this is a lasting interest and not a fad. I’d also suggest the “EF Lens Work” book (Amazon link or downloadable PDFs). This is a rather technical book, but does a great job of explaining the differences and why one lens is “better” than another for some purposes. There are many. many editions of this book (CPS members used to get the latest edition each year, until Canon got cheap). But even older editions cover the technologies involved, even if the specific lenses have been superseded.
In general, more-expensive lenses will provide one or more of:
[ul][li]Better low-light performance[/li][li]Image stabilization[/li][li]Faster focusing (useful for sports and other purposes)[/li][li]Quieter focusing (useful for wildlife photography)[/li][li]Tilt, shift, or tilt/shift features (think “shoot around objects as if they aren’t there”)[/li][li]Longer range of zoom[/li][li]Better image quality (for some characteristics - DO glass, bokeh, etc.)[/li][li]Impress your photography friends with how much you spent (mostly kidding here)[/ul][/li]To address some other points:
There are a number of 3rd-party lens manufacturers. In general, those lenses will work with the current crop of cameras. In the past, when a new camera model has been introduced, some lenses have had problems working with the new model. In many cases, the lens manufacturer offered a software update or a trade-in. But some people got stuck.
There are places which sell used lenses (and other stuff). Here in the US, B&H has a good reputation. They sell new, new out-of-region (gray), and used equipment.
If there’s an ongoing interest and the lenses will be useful for years, give some thought to compatibility with future camera bodies. Most of these issues stem from the less-than-full-frame sensors in some camera bodies - a zoom lens that is “just right” for one will not have the same coverage on the other. Also, the EF-S lenses don’t fit most non EF-S camera bodies.
…I hated everything about it. It was the complete opposite of everything I wanted in a lens. Some people are better off with the kit lens rather than dealing with 50mm on a crop sensor. It didn’t teach me anything at all: it was just an exercise in frustration. Just posting this as a counterpoint: as the 50mm is alway recommended as a “must get” for beginners and it is a really affordable lens for what you get, but it isn’t for everybody.
I also got advice to buy the 50 1.8 when I was starting out and did so on my crop sensor. I hated it. Very badly. My primary purpose was taking better family shots in the house and as a beginner I latched on to two things that I later discovered didn’t suit my needs.
First, I thought that the better low light performance would mean I didn’t need to use a flash. Well, at 1.8 you have very little margin for error in your focus plane, and kids rarely stay still enough to get that shot. Focus speed being slow on the lens, and the body I was using, this was frustrating.
Second, apparently the 50mm is great for portraits on a full frame sensor. There is a world of difference between what is good on a full frame vs. what is good on a crop. And ‘portraits’ are a far cry from shots of kids in action. It felt like I always needed to back up and I ran out of room in the house. This was very frustrating.
I quickly sold the 50mm 1.8 for about the same price I bought it for (best part about it!) and sprung for the sigma 30mm 1.4. With the 1.6x of a crop, 30mm works out to pretty close to 50mm on a full frame. Best lens I ever purchased for the crop sensor. If someone is starting out, and their primary purpose are shots indoors of kids in action - the best purchase isn’t a lens…it’s a flash and a radio trigger.
*now that I use a full frame, I did get another 50mm - though this time the 1.4. One thing that hasn’t been mentioned here…buying lenses and new gear is like a disease. It gets expensive very quickly 
I bought a Nikon D7100 last year and was told to get the 35mm instead of the 50mm, because of the cropped sensor. It’s been a magnificent lens for me to learn on, but would I have been better off with the 50?
ETA: Based on the responses here, I guess not!
There’s no doubt that it’s not for everybody. No lens is. I shoot full frame, and I don’t own a 50mm myself. I find it a pretty boring focal length. (But I do have it covered on my 24-70mm lens.) On a crop sensor, though, it’s a solid lens for portraiture. It’d pick it over the kit lens if you sent me out to do portraits with an 1100D. In my opinion, it’s a good lens to learn low light photography and low depth-of-field photography without making a huge investment.