The welder linked above is what I use. For $70 its worth it. You can keep a mank boat going for a while with a welder. Good tool, good price, easy to use, and the small tip is precise. You can also weld with a heat gun ($20-25). Its not as precise as the small tip, but you can rig up a small diameter tip using thin metal and a hose clamp.
As for the set up, the welder is really the only tool you need specifically for welding.
For welding rod material I use cut up pieces from an unrepairable boat. I cut 8-10" long rods out of the hull that are as wide as the hull is thick. Consistent width of the rod helps get a uniform weld. Cockpit shavings can work in a pinch, but everywhere you have shaving to shaving connections you have a weak point in the weld. Welding with continuous rod produces a stonger weld.
Welding on the inside and outside is stronger than just one side. For small cracks ( <3 inches) that are not in a high stress area (ie under the seat), I think a single outside weld is fine. For larger cracks or cracks under the seat, welding on both sides is key.
You can use wax paper to smooth out a warm weld. Put one side of the wax paper on the boat, fold the paper over so both halves of the fold are over the weld and smooth out the weld with your hand, putting some pressure and rubbing back and forth. Wax paper to boat shouldn't move to smear the weld, but wax paper to wax paper slides to allow for a nice smoothing out process.
After welding, putting some bitchethane on the inside can help stop leaking if the weld gets a crack in it. Bummer about bitchethane is that impurities make welds weaker, and its hard to get the bitch off once you have put it on.
I also check the boat after every run to look for new cracks or cracks in existing wells. Once the cracks start coming, more are bound to show up.
Nice work on the mank boat Jace.