I'm going to disagree with Scott on some things and agree on others.
If you want a welder so you can be a weldor and fix/make things from steel, then go for it, but for somethings that are very mission critical on your tractor, get them fixed by a professional welder.
The first thing you should do is learn something more about welding, look around I'm sure there is a night course that you can take that will give you the basics, and then you will be able to understand the difference between the four main electric methods.
Here are my impressions of the various kinds of welding and what I think are good and bad points about them
SMAW Shielded Metal Arc Welding
Stick welding You can, with the right rods and an AC/DC machine weld a LOT of different metals, but it takes real skill and know how, plus you have to keep those rods in good shape, which usually means a rod oven that is on a certain temp 24/7, not exactly for the home hobbyist. That is why most stick welding done by hobbyists or farmers is on metal, using basic rods like the 6010 or 6011 they work well on most anything, have good penetration and don't mind a dirty surface. The 7018 is good too, and you can make much nicer looking welds, but they need a clean surface and don't penetrate as well as the 6010/6011. Stick welding can weld through paint and rust and deal with wind outside. Really it is not hard to learn stick welding, but to become very good at it takes a steady hand and a lot of practice. Upsides are that you can weld thicker material with a fairly basic unit, 220V for sure but most homeowners have that on hand, even if you have to wire in a new 220V outlet. Also a good basic unit can be had used for very little money, older units might be a bit on the heavy side, but they are usually well made and will run for many more years. Down side, they are messy to run, chipping the slag, and they are not easy to use on thin material. When you finish the weld you have to chip the slag off the weld, this is the stuff on the welding rod that vaporized during the welding creating the gas cover for the welding pool and then protects the hot metal from contamination as it cools, this is messy but for outdoors welding on rusty painted metal it works rather well, and if you are out fixing a tractor in a yard, the mess is not a concern.
FCAW Flux Core Arc Welding
MIG with flux core wire and no gas bottle, in many ways this is like stick welding with a stick that never gets shorter as you use it. Basically there are the 110V and the 220V units, many are dual voltage, so you can weld 110V at almost any regular outlet, all be it not the thicker materials. The main difference is the thickness of the steel the 220V unit can weld over the 110V units. IMHO don't buy the 110V unit, unless all you wanted to do was restore a car body, even then I'd suggest GMAW unit even if it is 110V, as it is cleaner, no slag to get rid of. As Brent will tell you, the cheap 110V units are expensive, as they just don't work very well and you either give up, which is a waste of your money as you sell the unit for cheap, or it takes up space in your garage, or you still want to weld, so you end up buying a good quality unit that you should have bought to start with. This holds true for almost any tool, as I'm sure most of us are painfully aware of. Good points, machines are usually less expensive, this is fairly easy to learn how to weld and you can weld in almost any place that has a 110V outlet. Bad points are you are limited to steel and fairly thin steel, but they work and fill a need for many hobbyist.
GMAW Gas Metal Arc Welding
MIG with solid wire and a gas bottle. With a 220V unit and the right wire you can weld from very thin steel 24 gauge to 5/16" on a single pass. Machines like the Hobart Handler 190 are great, they also can weld stainless, with a different gas bottle and wire, and Aluminum, also a different gas bottle, wire and a spool gun, but there many package deals that the spool gun comes with. I think Brent got a Hobart....? By shutting off the gas, and changing the polarity of the welder (5 min job) as well as getting a spool of Flux Core wire you can also FCAW with this welder, which means you can weld outside. Some of them are also dual voltage you you can set it up to run on 110V as well, which means you can still weld even if you don't have access to 220V power, say at a friend's house or something. Really if I had to had to suggest one machine for someone beginning to weld I'd say a 220V GMAW (MIG) welder with the gas bottle, you can do a LOT with one of these welders, and if you want to sell it at some point you will get good money for it, because it is a very capable machine.
GTAW Gas Tungsten Arc Welding
TIG Welding. Like Bryan said it is very much like gas welding, without the fumes! Dependent on your machine you can weld anything from razor blades to fairly thick steel. The TIG welder does take the most time to learn and it is certainly a learning curve, but with an AC/DC machine you can weld just about any metal that conducts electricity, steel, stainless steel, aluminum, titanium, brass, copper, bronze, cast iron and I'm sure there are some I've not mentioned. The good machines are not cheap, but they are worth it, the arc is very stable and easier to use. Good points, clean, quiet, not such heavy fumes, bad points, steep learning curve, slow, not cheap.
If I could only own one welder it would be a TIG, as most TIG welding machines can also be set up to run SMAW or Stick welding too, that being said, the TIG is slow, if I have a bunch of basic easy welds to do, the MIG, GMAW will be my go too machine.
I hope that gives you some more info, and clears things up.
I'd not buy an offshore machine, lots of guys do, but I've heard some real horror stories about them, I did a LOT of research on the subject and I would not buy one of those machines, I'd look for a good used MIG welder with a gas bottle, or step up and buy a good new machine, Hobart and Miller are the top two IMHO as well as Lincoln.
I really think you should save your money and go take a lesson at a night school tech college of some sort, then make a decision of what works for you.
PS don't skimp on the helmet and gloves when you get around to buying them, good fitting gloves make the whole thing much easier to do and a good helmet is worth the money.
I like Chucke2009's videos, very entertaining and lots of good info.