Well this all depends on what kind of Welding you're looking to do. Also you need to define cheap. A good loose rule of thumb is 1 amp per 0.001" thickness of material. Harbor Freight (Horrible Frieght) makes these Flux Wire MIG welders that don't require gas bottles. They're $100 and change for a 90 amp, they say they can weld up to 3/16" material but I think that's a stretch. Best to read reviews.
hfreviews.com is a good place to check on stuff from Harbor Freight. Some of it's gold some of it's junk. You can get Hobart welders in the more $300 range. If you guys have a better idea of what material you want to weld and what the cost is then I can check with some of the guys I work with. Assuming Mild Steel and for ease of use I'd get a MIG welder and just make sure there's a place in town you can get bottles of shielding gas, unless you get one of the Flux Wire models that don't require gas but that seems fishy to me. Plenty of reviews and videos online about em, I just haven't really looked into them. Really the most important thing to look at is price. Once you know what you want to spend then I'd shoot for a MIG welder with the most amps, gonna need to get sppols of wire for different materials, probably best to get one for steel one for aluminum.. Don't forget an auto darkening helmet, welding (leather) gloves and possibly a welding jacket, if you're wearing short sleeves and you're pale and hairy you're likely to get sun burnt and light your arm hair on fire. Harbor Freight is probably the best way to go on the cheap, but if you want a better welder that's still inexpensive check out Hobarts or see what Sears is slinging now a days.
If you guys let me know material and cost I'll talk to the guys I work with and see what they recommend. Ideally though you'd buy a Miller or a Fronius but I can't see that being in the budget.