An AC only buzzbox is hard to beat for the backyard/farmer based welder. A lincoln AC 225 (the most common buzzbox welder of all time), Miller Thunderbolt (probably the 2nd most common buzzbox of all time), or Hobart Stickmate (currently made on same assembly line as Miller Thunderbolt) are a must have item for a crude backyard based shop in my opinion.
An AC buzzbox such as these units will actually do more than a welding alone. You actually have a very inexpensive mutipupose tool: Obviously they will weld metal (1/16" thick with practice and above of course), they will also cut metal (stick a 6011 in the stinger and crank the amps and you have a way to cut sheet and pierce holes). Also, build for nearly free or buy a factory made Twin Carbon arc torch for the AC buzzbox welder and you have a way to intensely heat metal for bending, freeing rusted nuts, brazing, silver soldering, flame fill welding, etc in a manner that does not require a gas based oxy/actylene based torch. Twin Carbon Arc will NOT cut metal so do not confuse it with carbon gouging which is a different process. Twin Carbon arc can produce a flame up to 1000 degrees hotter than oxy/acet can and do it cheaply.
These welders are as simple as it gets and there is very little to ever go wrong with them. I personally would not buy new one as plenty of used ones to be had for $75-$125 used on Craigslist. (If you add a little more money to the pool then you can even find same buzzbox with DC capability added for another $100 or so used but there is a little more to go wrong on DC capability units but worth having though). If and when you ever outgrow this welder then it will never depreciate and will still easily sell for the $75 to $125 that you paid for it. Personally, I will never get rid of my AC buzzbox as it is worth keeping around to power my Twin Carbon arc torch alone - even if I never used it for anything else.
Mig or wire feeders have their place too (primarly thin metal on cheaper priced Migs wire feeders) but they can get expensive too as there are simply more consumables. (gas if using Mig, tips for the gun, liners for the feed hose, feed rollers etc.). Mig or Wire feed with flux core is probably easier for a newbie to learn but it is a more limited tool in my opinion. Mig (with gas) has to be done indoors or wind blows shielding gas away. You can switch to fluxcore wire that does not use gas but then it will not weld as quit as thin of metal as Mig can - but you do gain some penetration on thicker metals. Flux core is not suited for body work - flux makes paint peel/bubble. Yes you can get wire feeders that will handle thick metal but they are big bucks. Mig or Wirefeed requires that metal be clean so not best suited for working on old rusty farm implements and metal salvaged from outdoor scrap piles.
But it is harder to learn how to make pretty welds. I think all three ( four really counting flux core) processes have their place and their advantages, that's why all of them are still going strong in the marketplace. So you need all three! But if I were you, I would get a stick welder first, learn how, then get the others as time, needs, and money permitted. There you go, free advice... worth about as much as you paid for it:laughing: