I’m sure you can definitely teach yourself to weld. Other than 30 minutes of my dad’s time instructing me, and setting up my welder, I was on my own after that. He left me to start on my first metal framed building. It’s still standing. 
My dad taught me lots of skills growing up, but welding was the one that I appreciated more than any. But I’m convinced you can teach yourself by what you suggested, youtube and a basic book perhaps. Never went to school for it, or would be considered a professional welder, so take this advice from a hobbyist point of view.
I recommend learning stick first or perhaps just that only. That’s pretty much all I use still today. It’s better for those windier days too, if you plan on doing some welding outside, but MIG can be used here too with no problem. With TIG, and the argon gas used, you’d have to take steps to shield it from the wind. If you can stick weld, you’ll be able to pick up on MIG fairly quick after that too, although beginners tend to shoot out a lot of wasted wire at first. If you’re set on MIG, I think you’ll still be okay, and it’s a little quicker by not having to change a rod every so often. I read an instruction book that said, you can learn stick in about one hour, while TIG was about 40 hours. That sounds about right to me. It didn’t say for MIG, but anyway, just a little bit longer than stick, I guess. TIG is more of a specialty type welding, and especially great for welding up 4130 chromoly tubes on aircraft, and popular with race car enthusiasts too. TIG is top of the line and the most highly skilled.
Just a regular AC welder will be fine on most jobs that you will be doing for yourself. You don’t really need a AC/DC welder, although I have one of those, and the DC helps to get deeper welds that penetrate on heavier gauge metal, but AC works great, and if the welding is never going to be much more than1/8” thick or less, you should do just fine with an AC welder for most home projects. Miller, Lincoln, Hobart, these are very good brand names that I’m most familiar with. Beware of some off-beat brands, if you have a problem with those, some will have zero support on ever having any parts for it. I’ve probably got over a thousand hours on my Lincoln, only had it in the shop once, for something not too serious, I forget now what it was. But anyway, good welders are mostly bullet proof. The factory I used to work at all had Miller’s. I honestly don’t recall ever seeing a repair man in there for any of them after nearly 13 years of working there.
Anyway, back to stick welding. There are many rods to pick from, but I’d recommend one rod only for nearly all of your jobs. You can use a 1/8” thick 6011 rod on just about any job. The numbers all mean something, and there’s a nice little book that explains the significance which I’ll recommend at the bottom of my post. Or you can do a search engine that will probably explain too.
Always get a good ground. If you have metal that has primer or paint, it really helps to grind off and make it shiny where you are going to put your ground onto. It helps to grind where you’re going to be welding too if it has paint or primer on it, you want a good spark to get going, without having to fight it. Nothing is more frustrating than finding a stick that refuses to arc. To get it to arc, you want to strike it like a match, and then keep it close to the metal to continue letting it arc.
To start out, grab you a couple of pieces of scrap metal, and start practicing. Let’s say you have some thin gauge metal, perhaps 14 gauge (which is about 1/16”). Set your welder to 75 amps. That should do it, it could still be slightly hot or cold, you won’t know until you’ve done a few short welds, and then take a good look at it.
Once you’re up and running, you don’t want to be too close or too far away from the weld to maintain the arc to keep things going. If you’re sticking your rod to metal, you may not be hot enough, or it could be you need to back off a little bit more on the rod or both. If you’re blowing holes, you need to move your rod in more, or lose some heat, or both.
One other thing you can do is test the strength of your weld. Take two pieces of scrap metal, weld the pieces together. After you weld, take your chipper, and knock off the weld crust, clean it up more with the wire brush, and visually see what kind of penetration you got. I’ve used other rods before, and there were times, I was shocked after I removed the crust, how little penetration I got. With 6011, you should do just fine with it; never had problems with it. Never mind how ugly the weld is, you’ll be surprised how well ugly welds hold, but you at least want to test it before you get started on your project. Put it in a vise, get a sledge hammer and start beating on it, trying to tear the two pieces of metal apart. If you have a good weld, the metal will tear in another place besides the area you just welded. You want to strive on making your welds look good, but trust me when I say I’ve seen some ugly welds that actually held up quite well, so there is a bit of a safety margin.
You’re going to be blowing holes in thinner metal, even experienced welders still do this on occasion. You’ll need to learn a technique that can repair it. To plug a hole back up, what you do is weld the hole for about two seconds, then back off. Let it cool, to where the bright red goes away, usually about five seconds or so, then weld the hole again for another two seconds or so, then get off of it. This will continue to build up the weld again, and eventually the hole will be plugged. Keep the rod in close, you don’t want it to flare on you, or it will make a bigger hole.
Always learn to tack the pieces of metal in place first, before completing welds, otherwise, you’ll end up having a twisted pretzel.
Best book I found for welding basics that has been out for decades is this little red one put out by Forney. It’s excellent! All welding shops locally probably have it too, besides Amazon. Welding pieces on a table or flat surface are the easiest welds. Welding vertical, or upside down, takes a little more skill, but how you position your stick will make quite a bit of difference. That little book I recommended covers this, and I believe all of the other stuff I mention in this post, but I’m sure will explain it a lot better. I think it will give you plenty of confidence. I learned quite a bit from it even after my dad taught me. My dad covered most of what was in there, but it was also gave me something to reflect on, and go to when I needed some help on a particular aspect. It will show you what a slow, fast, hot, cold, and other welds look like, and once you start recognizing this, you’ll be able to concentrate on making better looking and stronger welds.
Another neat trick I learned is drilling holes with welding rods. This really has come in handy. Do it just right, and you won’t even need to do any grinding or deburring. Sure beats dealing with drills and wearing out bits. The Forney book will show you the right technique on how to do this. It’s one of the easier skills to learn.
I really don’t know and not qualified to answer your last question about how to keep from getting electrocuted, just know welding is actually very safe, and has a great track record for being so. Been around welders all of my life, and I’ve never known any that seriously hurt themselves. Mainly protect your eyes, and try to avoid flash burns. There are times, when welding outside, and when the humidity was very high, and perhaps a slight mist, I could sometimes feel a slight tingle, so I avoid those situations. Even inside on high humidity days, I have felt it.
Well, I think I covered the basics. You’ll never regret learning this skill if you decide to go through with it.
