I think that’s a sound idea. Going from *no *camera to a camera with one zoom lens is a definite step up. And the money you save can go into a decent bag and a nice big memory card.
Hmmm… I actually have that Tamron wide angle for my Canon T2i. Plus, I had the 55-250.
I find that about 3/4 of the time in telephoto I am shooting at full zoom - meaning I want to get a picture of something a long, long way away. Actually, the difference between 250 and 300 is not that great.
I later bought a Tamron 28-300 -it’s nice because I don’t have to keep changing between regular and tele. But, that would blow your budget. The only annoying thing is if you don’t lock it when just walking around, the lens extends from its own weight and you look like an bull elephant in mating season.
Remember that there’s a rule of thumb about length vs. shutter speed, but basically for full zoom she needs either bright sunlight, nerves of steel, or a tripod. the slight handshake movement we all have will cause blurring at most shutter speeds; if she can’t hold steady for long enough, the autofocus may not work. So a tripod may be the logical consequence of wanting telephoto. IIRC, the conversion factor for Canon Rebel is about 1.6 or so, so 250 works out to 35mm equivalent of 400mm. That’s plenty of tele.
The advantage of a wide angle - you can get great architectural photos or group shots. With the Tamron at 10mm, you can take a photo of a NYC brownstone, 3 stories, from the other side of a narrow street.
(One little oops; I had the 2 kit lenses for the Canon, then the Tamron. The plastic lens back for the Canon does not fit the Tamron, or vice versa. TO carry around all 3, I had to buy a second Canon lens rear cap. Fortunately, in NYC you can find anything in stock and at a good price.)
So then you’ll need a camera bag, and depending on your holiday plans, see how fast you go through a battery and decide if it’s safer to have a second battery. I decided when I was playing tourist in China or Australia it was better to splurge on a second battery that irretrievably miss some photos because the battery was dead. However unless you go crazy, it generally will last 2 days give or take. Charge it every night. Each photo is about 4 or 5 MB so a 16GB or better card is a good idea for a holiday.
And when you do, look at the macro ratio; if it’s anything greater than 1:1 (for example, 1:2 or 1:4) it’s not a true macro, just a lens that focuses close. A good true macro will be costly, probably as much as the camera body itself. (Rule of thumb: buy cameras, invest in lenses.)
The kit 18-55 should be good to start, waiting on the tele zoom is a good idea. 18-200mm is a bit long for a zoom; image quality will suffer at the extreme ends. Any zoom greater than 3x really needs quality glass for quality results.
The general rule of thumb is that you can hand-hold comfortably at 1/focal length of the lens (35mm equivalent). So, with a 200mm lens, which is equivalent to a 320mm when placed on a 1.6x crop sensor like the T3, you can handhold at 1/320 sec. Steady hands can get this down at least one stop (to 1/160 sec), if not two (1/80 sec). Also, any image stabilization should help you out 2 or 3 stops. That said, remember that it’s not only your movement that affects the image, but also your subject’s movement. If somebody is running across your frame, it doesn’t matter that you can hand hold 1/80 sec on a 300mm lens–you’re going to get motion blur. (Subject motion blur is not necessarily a bad thing, but it is something to be aware of.)
Frylock, just be aware that photography is subject to developing Gear Acquisition Syndrome. No matter what gear you buy, the next day you will be drooling over even more advanced stuff with prices just out of reach, and then you will decide to take a second mortgage to be able to get that just-one-more-piece-of-equipment. And this will never end.
So I commend your choice to start with the kit lens and go from there. 
Your next step after that could be:
[ul]
[li]More lenses to extend reach[/li][li]A lens upgrade same range as the 18-55 with better optics for better image quality[/li][/ul]
And, of course, if you ask 10 people you will get 10 opinions.
BTW I have the 70-300 that you looked at for my Canon 20D. It is a good lens at that price point, though as I gained more experience I started noticing the flaws in the optics.
My vote is also to defer purchase of another lens. Of much more use is a spare battery. The time between “Battery Low” warning and “Battery Dead” is very short. Non-OEM batteries are much less expensive and usually work as well as brand name batteries.
I have a Sony DSLR with 18-200 and 75-300mm budget Sigmas (the 18-55 kit lens broke after less than 18 months). I can’t justify spending more on quality glass, but my results with this kit have got me published a few times, so I’m obviously doing a few things right! I would echo the comments of others who said that the wide angle lenses offer more. A friend has a Sony mount 10-24mm which he is kind enough to let me borrow, and the results with this lens are much more eye opening than any advantage you can get with any amount of increased zoom, within sensible budget constraints.
In return, I occasionally lend him my big flashgun, which is something I would suggest you consider. Even for everyday (daytime) shooting, a big flashgun has a subtle but very noticeable effect. It also offers the versatility of moving the unit off the camera and opening up all kinds of different lighting possibilities. For the price of another budget lens, it is well worth considering.
When I got my 500D (?T1i in the US) I had the choice of a two-lens kit or the 18-200. I went for the kit which had the 18-200 and it served me well for a long time. I still use it if I don’t want to be switching lenses all the time and it may be worth seeing if that kit configuration is still available with the newer camera.
This was a very wise decision. If this is your wife’s first dSLR her first task is to get acquainted with the camera’s capabilities (good choice BTW). Then, depending on her interest, you can buy additional lenses later. The 18-55mm is a good (but not the best) walk-around lens. It should serve your wife well as she learns the camera’s many capabilities. You do realize that you have embarked on a path of many potential camera add-ons: filters, tripod, memory cards, camera case, not to mention all those new lenses!