phew here we go
OK, the simplest welder to go with is a cheapo ebay flux core wire feed welder, every muffler shop around here uses flux core and it will last a good while (usually 5+ years when you get the technique) I just bought a 125 amp flux core welder for 100 shipped off ebay, it works great. Also check out Lowes outdoor section for some metal post tubing, it is $12 for a 12 foot section and it does not rust, it comes in mutiple sizes and the $12 is for 2.5 inch pipe. Speaking of which the flux welds will rust no matter what you do, dont sweat it if you have the will to make your own exhaust you have the will to fix it a while down the road.
Edit: heres a little more info on different welder types, a cheap welder will last a while, but if something breaks generally its cheaper to just buy another one, the more expensive a welder and a name brand will usually mean it lasts longer and comes with a warranty and support later down the road.
you can guy a gas welder, a wire feed welder, or a combination. The combination usually comes with a gas adapter you can buy to do real mig welding. As far as the differences mig welds and flux core welds go, the gas is used as a shield againt the air we breathe and will help prevent the weld from rusting. Instead of using gas a flux core has whats called flux in the wire that shields the weld when the arc is started, but not as well as gas will, so the weld tends to rust a little and you end up with slag and spatter around the weld that makes it look not so good. When you get good enough you will end up with less slag and spatter. personally since the exhaust is under the car I dont care to use flux.
Hope this helps!