yeah, those transfer papers you buy from the store are a joke.
for heat transfers, we have an oki printer and use magictouch transfers. for sublimation transfers (when the damn thing worked) we went through sawgrass technologies for ink and paper, as i recall, and use an epson workforce 30 printer. both have very real pros and cons and both require a heat press, which you can get online just by doing a search for 'heat press' and start comparison shopping.
depending on your art, plenty of screen printers can print more than just your basic 1-3 colour designs. ask some about what they offer ~ some will do a process colour, discharge, etc.. a popular option is looking into direct-to-garment printers. then there's the aforementioned vinyl.
a lot of people really like plastisol transfers. find a place that does these, and they'll put your design on a special transfer that you heat press, the result being just like screenprinting.