First, the most important part of any welding system is the man controlling it. There has been an amazing amount of stuff welded together with an oxy/fuel torch or even carbon arc torches.
The only thing I wouldn't recommend a stick welder for is sheet metal. .120 roll bar is fine with an stick welder, I do that .125(1/16") all the time with no issues, the key is tight fitting. I don't use it on .065 chromemoly tubing, that I use my oxy/fuel torch or my TIG welder, normally the torch if its steel and the TIG if aluminum or stainless. I really recommend a DC stick welder as they are very smooth and striking the arc is much easier for a beginner. With some practice and some 7018 DC you will come very close to the appearance of Mig welding in smoothness.
A used Dialarc or Idealarc machine will do any thickness steel without issue for a price cheaper much cheaper than any decent MIG machine.
A MIG machine is the easiest to learn and the hardest to master. You can have wonderfull looking welds with it but they are little better than glue as they have no penetration if done incorrectly. I will not trust my life in a vehicle welded together by a beginner welder with mig as you don't know. I will with an stick welded cage as just looking at them you can tell if they penetrated or not.
I think evey shop needs an good smith or victor midgrade oxy/fuel torch. You can cut steel, weld any metal(with proper fluxes) in thin sections, braze, and strink/stretch body panels with ease. Welding steel with good fitting joints is obtainable with some practice up to .25". A good stick welder takes care of the heavy stuff, ie 1/16 and up.
No matter if you pick a MIG set up or A stick set up, get a 180+ amp machine, a 250 can handle any thickness with multiple passes. This means 230volts. Any thing less than 180 does not have the heat to weld .125 thickness metal and up. The MIG manufactures "welds up to ..." should be halved. A 110volt machine is good only for sheet metal. I know that some will disagree but I have fixed to many broken welds made with machines of this size.