I wouldn't say I taught myself, but I didn't have any formal training. I learned most of what I know from the generous folks over at Velocipedesalon. There is a wealth of knowledge over there and most of your questions have been answered there many times.
As far as what to splurge on, get a good torch. Regardless of what Paterek says, don't use a Mapp gas torch. I've done it and it can be done with silver, but it takes too much time to get the joint up to temp. and you can't properly heat a large enough area, especially on bottom brackets or fork crowns. Get a decent Oxy/Acetylene or Oxy/Propane setup and you will be much better off. And don't waste your time with that Bernzomatic Mapp/Oxy torch either. You will blow through those $10 oxy cylinders like crazy. There is some great info here about Oxy/Propane setups
http://www.velocipedesalon.com/forum...ane-30480.html
For frame design, download Rattlecad. It's free and it works pretty good. Make sure your design fits with the available lug angles.
For cutting and mitering tubes, get a decent hacksaw and some half round files. There is no need for a mill and hole saws for hobby building. Nova Cycle supply has a nice tube miter program that you can use to print out templates that you can tape onto the tubes. They are also a good source of framebuilding supplies
http://www.cycle-frames.com/bicycle-frame-tubing/
That should get you started.