[Three Peaks]

Any decent Mig welder should work fine. I'm a fan of the Miller line, but Lincoln and several others make very good machines. I used a Millermatic 130 for my build, but I was pushing it the whole time. If it were me, I would be looking for a 180 sized machine. Get the big tank 75/25 of gas, you'll need it. Filling the small tank gets old real fast and expensive.
Lots of good tube notchers around, also lots of cheap ones. I think I would look seriously at craigslist for one. I find lots of machine shops, fab shops, etc... shutting down or upgrading and I find lots of these tools cheap on craigslist in almost new condition, including the welders. Make sure you have a chance to try any welders first before buying if buying used. Sometimes the inner liner of the gun feed tube will be worn or the feed rollers need replacing and you can tell pretty quickly if you use it for a few minutes if they are balking a bit at feeding properly or the gun and/or trigger is working properly. Most of the time they are perfect, and are relatively cheap to replace if you get a good price on a used machine. Millers are almost impossible to kill IMO so that is the route I usually go.
Not sure what other tools you have or don't have so hard to advise as you seem to have a pretty good arsenal at your disposal already. You'll need a good rivet gun, a metal brake, a good cleco set, and a good supply of #30 drill bits in good quality. I think I installed well over a thousand rivets in my build.
A good sheet metal shear is helpful but that is down the road after the mechanical stuff is done.
Here is where things get interesting. Depending on where you get your body, you won't know where to mount door hinges, birdcage, or a lot of the mounts until you have the body. A lot of the "original" bodies that these bodies were splashed off were assymetrical, so the sides don't match. My body is splashed off an original supposedly and the driver's side door opening is 2" closer to the front of the car than the passenger side, along with a few other locations. Even the wheel openings may or may not be in line. No two cars were alike with the originals.
Kirkham got around this by splashing an original and mirroring one side to the other so they match exactly. Best idea so far, if you are going to buy a Kirkham body. Otherwise, you will have to work with what you get. Lots of other little intricate little details to work out like the body supports around the rear wheel arches, roll bar suppport brackets, etc... that can call be done after the chassis is assembled and ready for the pieces.
I almost miss the project now....

Bob