Great question, don't think I've seen any threads about welders...
IMO the 'easiest' welders are something you can power off normal house power (i.e. 110volt) outlet. I had a Lincoln WeldPak 100, which worked great, it comes setup for flux-core welding, which is basically the wire-feed version of stick welding, where the flux (what cleans the rusty metal and helps the new added-in metal to stick) is already built into the welding process, so you just turn it on and go. The downside to this is the welds aren't as pretty and clean always (splatter, which is little molten bits of metal that kinda fly around and like to stick to about anything, especially skin). The upside of fluxcore welding is because of the thickness of the wire (0.035" typically for fluxcore wire) you can weld thicker metal than a same-power-rated welder would welding with the other process which is MIG (metal inert gas) welding. With MIG the wire is just pure wire, no flux in it or anything, to keep the weld from oxidizing too fast, as you weld the welder sprays out a shield of inert gas (i.e. something that won't oxidize metal) around your weld. This works to keep your new weld nice, pretty, strong, etc..the downside is this is not a replacement for flux as far as cleaning dirty metal during the welding process, so a MIG setup requires a much cleaner metal to start on, the welds are stronger than flux-core (since there is no flux mixed into the molten stuff), but the welding area has to be clean to get the weld to stick at all.
A stick welder is cheap and (for the price) very powerful, meaning you can crank it up and burn through some serious steel. However, for general purpose welding I think a wirefeed welder is soooo much easier to learn and more practical.
Many welder can be converted from fluxcore mode to MIG mode by adding a internal solenoid kit (to turn the inert gas flow on/off) and a few other bits. I did that to my WeldPak 100, which was nifty (MIG kit for it was ~$90 at Lowes), but it couldn't weld as thick of steel (and it can't weld terribly thick anyway), so that made pretty welds, but not really all that practical.
As your skills grow is a iffy area, since it all depends on what you're welding, I know 30+ year experience welders who love to weld on their cheap 110v welder, it's easy and the actual welding itself is all about technique, a good welder (person) can make a cheap piece of equipment seem great, and a crappy welder (person) still can't make good welds with top notch equipment.
Personally I would look at buying a Lincoln 110v welder, many on ebay, small, fun welders, 3 yr warranty when bought new, etc...
