I started with stick welders and oxy-acetylene torch, then welded with a flux core welder for a couple years before I got a MIG welder. MIG leaves a cleaner weld without much post weld cleaning.
Funny that no one has mentioned oxy-acetylene torch, I've seen used torch rigs sell for less than $200. The learning curve is steep, a bit harder than stick welding. But once you master the torch you can weld or braze almost any metal.
Stick welding has a much harder learning curve than MIG or fluxcore. Most of my students can learn to make a decent quality MIG weld with about an hour's practice and some coaching. Back when stick was still in the curriculum, that took about 3 hours.
If you ever want to stick weld anything thinner than 1/16" thick, it's not all that easy to do without burning holes. Depending on the machine and set-up, MIG can handle thin metal down to 24 gauge or so, flux core down to 20.
But as long as you are welding thicker metal, a stick welder can weld just about anything with the right rod. And there's the catch, if your rod is not kept dry stick welding can be frustrating and miserable. Some rod can be baked to dry it out, some is just ruined if it gets to absorb moisture from the air. We have to stick weld so seldom now, I just buy new rod right before each project, but rod is more expensive in small quantities. If you want to have good rod always ready to go, or buy in bulk, then you'll need a rod oven.
Flux core wire needs to be kept dry, but it won't go bad when exposed to humidity the way stick rod will. MIG wire keeps forever if you keep it somewhere dry enough that it won't rust. 100% CO2 shielding gas works just fine for steel and is cheaper than argon blend.
You might get lucky and find a good used welder in your price range, it boggles the mind a bit to think that a new $200 MIG welder could have enough quality built in to be worth buying. I can recommend a book that costs about $20 though: Welder's handbook by Richard Finch
