Mig welders will do anything you need in cart building, matter of fact it is a lot easier than stick welding for building frames. I have welded 1 1/2" plate with a mig welder.
Gas gives a much cleaner weld than flux core and solid wire is cheaper than flux core.
What welder to buy depends a lot on your budget however I don't recomend buying a cheap welder just because that is all you can afford, wait a little longer and save up some more money and get a good quality welder, you'll be much better off in the long run, it will last a lot longer and when the time comes you'll be able to buy parts for it.
You can get a smaller welder if that's all your budget allows but just don't go cheap.
I personally prefer Hobart but your best welders are Miller, Hobart and Lincoln and I would recomend not going any smaller than a 140 amp.
If your going to buy a larger machine then keep in mind you are going to need 220v, 140's and 180's you can get 110v, which for lighter welding is fine.
I have welded up to 1/2" steel with a 140 amp 110v machine, it's not practicle nor recomended but can be done, a 140 is rated for a max thickness of 1/4"-3/8" steel.
There is a product called anti-spatter spray which you can spray surrounding area's with to make cleaning up much easier even if your using solid wire it is still a good idea to have a can or two on hand, also get tip dip, you dip the tip of your gun in it and it helps extend the life of your tip and nozzle by preventing spatter build up in/on the end of your gun.
Hope that helps, feel free to ask anymore ?'s.
blksmith19