I've done lots of frame hacking in building (weird) bikes and scooters (see
http://www.outsideconnection.com/gallant/hpv/ ). My own tools of choice are as follows:
An oxyaceteline setup for brazing, not welding. Brass is easy to work with compared to welding. I like to use brass rods that are precoated with flux, rather than bare rods with paste. If you braze or weld, work in a well ventilated area as flux fumes are poisonous. I bought my first welding setup at a pawn shop for $50 and have since replaced the hobbyist sized bottles with bigger bottles, but still use the original hoses, regulators and torch. Don't be afraid to take a welding class. You'd have fun. Brazing is really fun.
I like my Harbor Freight tubing notcher. It needed shimming, but it's worked well for me. The hole saws that I bought for mine have worked well for years. Get decent ones. Use cutting oil on them when cutting tubes. Go slow. Wear eye protection.
You need a drill press for the tubing notcher, but you need one for other stuff anyway. They're all made in Taiwan now pretty much, so take your pick.
You should collect as many files as you can. Collect different profiles (flat, half round, round, triangle, etc.), different grades (course, medium and fine) and different sizes. I use golf balls for file handles. Learn to file. It's an art. Files like hacksaws only work in one direction.
Collect clamps too. C clamps and bar clamps. Go to yard sales for this stuff when you can.
Get a decent bench grinder, and the stones to clean up the wheels with after heavy use. Use it to remove lots of metal fast. Watch your fingers and hands.
An angle grinder is extremely handy. Cleans scale off of metal before brazing really quickly. My $17 jobber from Harbor Freight works great, but is really noisy.
A belt sander is super handy for removing paint from tubing before brazing or welding it. Also handy for making cuts at the ends of tubes square, as it grinds metal to an extent. You can press a piece of tubing against the right angle guard/brace piece, then down onto the moving belt to get the square end. Rotate round tubes when you do this and you'll get a squared off end. It wears the belts quickly though. I usually file most of the paint off used tubes first, then hit it with the belt sander.
I'm more of a fan of reciprocating saws with metal blades than chop saws. My Makita can get in tight places and can cut pretty thick metal with a decent blade. Buy blades in bulk, they're cheaper that way.
Make or acquire a big, sturdy, smooth, flat and level bench. I built a sturdy one out of wood, then fastened two sheets of cement backer board onto it with screws for heat protection, then screwed down a big, 3/16" piece of plate metal I bought at a salvage yard. I braze, weld, and hammer on this thing. It's great.
I got a Drill Doctor for xmas a while back and am still trying to determine if it does a decent job or not. I have friends that sharpen bits by hand on a grinder. I've tried that but haven't developed the touch yet.
On tubing, collect old bikes for tubing. They're free all over the place if you're patient. If you resort to using electric conduit tubing like I do at times for odd stuff, file or grind the zinc coating off before applying heat. The zinc coating is poisonous.
More later if I think of it.