To throw something else into the mix... I really like TIG brazing. You only need a DC machine, which is cost effective in itself, as well as the gas and rods. If you have a DC TIG set. It's a no-brainer. If you don't, it might be worth considering that against the oxy kit and future plans. No special torch or anything needed, just standard consumables. You must get the TIG brazing rods, though! The ordinary ones with zinc in explode in a heavy metal fireball.
The process itself is lovely. Heat where you want the braze applied, apply the rod until it flows into the workpiece, move on, repeat. No need for flux, flames or loads of heat. Far, far easier that fusion welding with TIG, but a great skill builder as everything happens fairly slowly.