If you want cheap, find an ac "buzz box" (stick welder). The learning curve on stick welding is a little steeper than MIG, but if you can weld well with stick you can weld anything. I see used ones advertised around my area all the time for 100-150 dollars. Just make sure you get the proper sized welding rod for the welder (make sure it is for AC if that is what you are using). You also asked what we use. I use a MIG (Miller 135) with hard wire and 75-25 gas. The welder is a little under powered for what I use it for, but I am a fairly good welder. The only welds I have had break were shock mounts on a TJ 8.8 conversion, and they were due to the shocks bottoming out severely (too long). I also didn't have the access to the rearend to weld them to my satisfaction, but could not persuade my friend to pull the rear end out for me to do it better. If you want to spend the money, a 175 amp Mig welder would be ideal. For cutting I use a friction saw to make the straight cuts, a torch or my newly acquired plasma cutter for cuts that aren't straight. A little more detail on what you are planning to do and I can help steer you in the right direction
JJ