Recently I asked on the 23b mailing list about welding tools, with the goal of gaining some insight into the various options to get started with welding at revspace. The below text was Arclight's response, which I think is a waste not to share with the world.
Gas Welder (aka Acetylene torch, Smoke wench, gas axe)
This is the simplest type of welder and what most apprentice/trade school programs start you out with. You buy a set of regulators, hoses and accessories and then you can either purchase or rent the gas tanks. With a welding and cutting head and the right tips, you can do anything from Silver soldering a charm on a bracelet to welding 1/4" steel plate. You can also cut steel that is up to 2" or more in thickness. It takes some time to get good with the gas torch, however and it's slow to use. Filler metals and braze materials are added using a stick of material that is dipped in the weld pool with your other hand.
Expect to spend US$150-300 on a setup, and additional money to rent the tanks (here it runs about $20/mo). Used ones are often available cheap.
Stick welder (aka Shielded Metal Arc Welding, buzz box)
This is the next most basic welder. It consists literally of a transformer, some cables, a ground clamp, and an electrode holder, also called a stinger. The welding is done with a consumable electrode clamped in the stinger. The electrode is a piece of steel wire that is coated with a flux which burns and creates slag and shielding gas to protect the molten weld pool. The better models have AC and DC capability and are easier to use. The cheaper AC-only ones also work, but require a bit more practice to get the arc started. A stick welder can handle anything from thick sheetmetal to welding 1" or thicker plate with multiple passes. Things like bridges and pipelines are still made with this type of welder.
Expect to spend US$200-500 on a new one or about half that used. One nice thing is that the only supplies you need are rods (which are available everywhere worldwide) and a place to plug it in. The filler metal is supplied by the rod as it melts away and becomes part of the weld.
TIG welder (aka Gas Tungsten Arc Welding)
This is like the Mercedes-Benz of welding. With a TIG welder and a bottle of Argon, you can weld anything from mild steel, stainless, aluminum, Titanium, etc. Someone who is good can weld two beer cans together, make a vacuum-tight connection for an electron microscope, or make two pieces of 1/4" Aluminum stick perfectly.
The machine consists of an electronic power supply (the nicer ones use inverters instead of transformers), a gas bottle and regulator, a foot pedal that controls your power output, and a hand torch which holds a Tungsten rod (not consumed). The machine operates like an Acetylene torch. You ground the work, step on the pedal, and metal melts into a pretty little pool under the tungsten torch tip. Filler metal is supplied by dipping a bare rod of the appropriate metal into the pool, before moving the torch. Make sure you get a model that does both AC and DC, as AC is needed for Aluminum.
Unfortunately, the TIG process requires quite a bit of practice to get good at, as well as gas, tungstens and filler rod. One cool thing is that pretty much all TIG welders are also stick welders. TIG is best for clean, virginal materials and produces beautiful and x-ray quality work. Stick welding is great for dirty, painted crap and still produces pretty good welds.
A quality TIG welder will set you back US$1000-3000 around here.
MIG Welder (aka Metal Inert Gas, wire-feed welder)
This is starting to become the most common welder in small shops. It consists of a power supply/wire feeder anda torch witha hevay sheathed cable. A gas bottle is optional.
The process works like this: Ground the work, pull the trigger, and wire comes out the tip from a spool. As it hits the metal, it shorts out, melts, and creates a weld. To weld something up, you just hold down the trigger and move the gun. You can teach someone to MIG weld in about 20 minutes, once the machine is adjusted correctly. MIG wire is available in solid (used with CO2/Argon gas) and flux-core. The gas version produces nicer welds that don't have slag on them, while the flux-core wire is better for welding outside or in drafty areas and saves the hassle of using a bottle.
For 80% of projects, a MIG welder is probably sufficient. You would be able to weld anything from car sheet metal to maybe 1/4" steel. The key here is that you're pretty much limited to using mild steel in your projects. There are special gases and wire for Aluminum and Stainless Steel, but AC and a special gun is required for Aluminum.
I would recommend a 220V model that takes at least 20A if possible. They make small ones which are great for fixing your mum's garden gate or railing but overheat quickly when you try to weld heavy stuff. Some models can work on low amps when plugged into a house socket and high power with a heavy-duty plug.
A good MIG welder here starts at US$400.
In addition to the machine, you're going to want to set up a work area with a strong ventilation/exhaust fan, a welding curtain to keep everyone from having to look at the bright flashes, some welding hoods (auto-darkening are nice), gloves, and non-synthetic long sleeve clothes. All of the arc-welding machines require a full helmet with a #9 or darker shade and all exposed skin to be covered up against UV. The gas welder only needs a #5 shade and glasses, as it's much less intense.
You might also want to think about how you're going to cut the metal you are welding. If you have $650-2000, a plasma cutter is awesome. Otherwise, a small horizontal band saw, a vise, and some hacksaws will do.
Avoid the temptation to buy Chinese welding equipment. Even if it's well-made, finding parts is really difficult. Welding machines and consumables are a commodity in every country. If you buy one of the common brands in your area (for here it's Lincoln and Miller) then you are assured of getting supplies and replacement parts at any shop and for many years to come. The brand-name stuff is usually 2X the cost of the Chinese, but it's worth it if you're going to use it a lot. There are some cheap MIG welders out there that take common supplies, so that might be an option if you're really on a tight budget.