I agree with Antichrist on this. MIG's are nice machines, but it's so easy for beginners to take a stab at the wire speed and current and lay down some beads and think they're welding, when really it's not much better than metallic hot-glue. I've seen some truly nasty welds on things that the owners should be embarrassed about, but they just let it go because it "works". A lot of this stems from shows on TV where you've got people MIG welding with no protective gear, they just close their eyes and spray metal everywhere.
I bought myself a Miller EconoTIG years ago and taught myself to weld. It does stick too, but I hate stick. I TIG everything, even my garage shelving. I've got a box of sticks that have been rotting in the basement forever.
I think learning TIG forces you to develop good habits. It won't tollerate welding on dirty metals. You must wear protective gear and use a helmet because the weld takes longer, there's no quick way about it, your filler hand is right in there, and you have to SEE the weld pool. I just love that you have live control over the weld heat, and the amount of filler you want to add. If you're doing a butt weld, you don't need much filler. If you are doing a fillet, lots of filler. If you've got a butt weld that blends into a fillet, then comes up on a edge, you can blend them all together on the fly and make a beautiful weld, instead of stopping to change settings.
I also like the TIG because you can weld anything. Steel, SS, Aluminum, or even into the exotics. The only thing it won't do is weld nasty old rusty dirty steel. But, if you're fixing up an old trailer, just use the stick mode on the same machine.
I just really wanted the option of welding aluminum, because it opens up the repertoir of what you can make. I just made a nice light bar for my truck out of aluminum instead of steel. Weighs nothing and won't rust. I've also done aluminum piping for car intakes and coolant systems, and some SS for exhausts.
Yeah, TIG is slow, but unless you're doing production welding. Who cares? The EconoTIG only has a 20% duty cycle, but I've only shut it down once. Novices spend way more time fitting than welding. Or at least they should. It doesn't really have high frequency or square wave, so the aluminum welding isn't great, but it works. I've made pressure vessels for coolant systems that have held on the first try. You don't NEED square wave for aluminum just for the basics. Just don't try to weld up a homebuilt aircraft with it...
My only regret was that for only a few hundred more, I could have gotten a "real" TIG machine with square wave, etc. But at the time I didn't know better.
The other thing is Oxy welding. It's a lost art, mostly because of the popularity of cheap spray and pray MIG welding machines. Gas welding is very similar to TIG, and the skills transfer over. The setups are cheap, plus you can use them to cut, and you can weld aluminum too. But nobody does it anymore because it's the hardest of all.