135 - 175 amp mig welder. you would need gas. your total investment would probably be in the 4 to 6 hundred dollar range. this would be set up for carbon. You can set it up to run stainless, but that would require another gas bottle (unless you only want to weld stainless), and more expensive filler wire. My lincoln 175 plus runs off of 220, but that was very easy to wire. My fuse box is in my garage, and was easy to set up a 220 outlet. i believe some of the 135's do plug directly into the 110 though, you will have to research that. a smaw (stick) machine is allot harder to use for that kind of work, especialy on thin metals like exhaust pipe. a gtaw (tig) makes a much prettier bead, but requires much more skill. Tig also costs more to run for both the machine and the consumables. I have used my welder for exhausts, intake manifolds, engine mounts, bumpers, turbo brackets, and roll cages.
you mentioned that this was for a project.... You can ask anyone, I am the last person to dicourage someone from looking into welding as a hobby or a career.... It is only fair to you that I say this. If you are going to buy a machine for this one job, with a slight chance of using it on another car project later on down the road, you may want to call a local fab or exhaust shop for quotes. Odds are it would be an awful lot cheaper!!
ps, with the above welder, you would also have the option of running fluxed cored wire instead.... and that would not require any gas. This would allow you to weld thicker metal, but would limit you on the thinner stuff.