I got my initial welding workshop at a welding citification training school / fabrication shop. A place like the one I went to works with individual students for basic structural welding up to nuclear reactor piping and aircraft space frame. If you can fine a place like this one they will train you to do a specific task that you wish to learn and on your specific materials. This is something you could find through the local welding suppliers "how i found my place". Tech school classes are great but you will have to spend many hours on tasks that will be far from your intended uses. But if you will be doing gas welding + brazing the bonus is that it is most likely the first things they will teach you. Also the skills from gas welding will help when you move to TIG. As far as welding machines I would buy the best you can afford, tig is going to be best for bike frames, the Miller Dynasty 200 DX would be the dream machine for your purpose if money is not an issue. For light use a quality welding machine will most likely last a life time.
As Peterpan1 has said the Gas system will do everything you need for frames and more.