I can't add much (and maybe will restrain myself from typing much). I have had a couple of arc welders. AC units can be had for as little as $50.
AC/DC will cost a bunch more. They add versatility as they can make different welds with little set up (just buy the correct rods). DC is much more versatile. But it takes a lot to learn to do well.
Wire feed welding is easier to master, with its own limitations (it is not for overhead welding, though you can often get away with it). Wire feed welding probably has several names for its various methods, but gas shielded is called MIG, and non-gas with flux core isn't. The cheapest wire welders are flux core only, and may have a very low duty cycle rating for the wire size they use (like .025"). Better machines will weld larger wire with longer duty cycles (x% of a ten minute time frame -- depending on local conditions like ambient temps & humidity, cool intake air, etc).
A lot of folks have made some good suggestions for machines. Name brand matters, as support for the various overseas products can be tough. There are usually several of the smaller wire fed Lincoln's in my local Craigslist. And plenty of the small arc welders (225 amp or so) units. As a machinist you are well aware of when paying too little costs more.
Airco, Miller, Lincoln, Hobart, Linde, and a few others, are all good possibilities. I have been looking around for a tig welder for a while. One of the things I noticed and came to terms with is that a lot of the large old arc welders (ac/dc usually) were the core machines for tig welders, and even if I didn't have the power to run one at full bore, I had plenty of power to run one at what I would need.
Personally, I have found my old AC arc welder rarely gets used, but occasionally I have that rusty/dirty situation, or really big piece that I either want to weld to completion, or at least tack it in place and see where I am going before coming along with the MIG welder (man, mig is so much cleaner than flux core). Some arc rods are very clean as well (I would say even pretty by the results).
The toughest part of all this is recognizing when the work has been done correctly, regardless of welding process. There are several welding forums out there (I think each of the major brand names have them in addition to others that are like this forum -- unsponsored). They can help you with info on any particular machine as you find them. Some are more throw away, others are more repairable (for example, my private label Hobart Handler 180 is NOT the same as a Miller of similar power, the Miller is definitely built differently/better). And there is a price difference!
You will also want to consider the cutting method(s) you will want to use. As pointed out, the Oxy/acetylene v Oxy/propane v plasma. Plasma is usually a second source as you almost always will want a way to heat and braze things. But is sure saves on weld prep time!
Buy yourself a good small side arm grinder (4.5"). It's easier to use and far less tiring than a 7 or 9" one (another second round machine). Plus it will get into tighter spots. You will likely want to have two: one to grind with, one with a wire brush for cleaning and slag removal. This is definitely where spending enough money matters (deals always count). Try Tylertools on line for prices on refurbished tools. Or Toolking.
Well, I typed more than I meant. Sorry.