Your options are sublimation onto light coloured garments, or print, cut and sew. Cut and sew you would have to outsource the printing. These would all have to be onto polyester.
Your other option is to screen print with waterbased ink. This can be discharge or standard waterbase ink.
Another option is plasticharge, a hybrid technique.
There is a new wave of screen printers who are able to produce some very high quality prints with classic plastisol ink. I print for a major brand here by hand. On the print I did today for them, the white has a slight feel or hand to it if you run your hand over it, but the other 3 colours are very very soft.
A retail shop compared my prints to the competition and said theirs were thick heavy prints and felt like wearing a glove, whilst mine were totally different. They print with an auto and I print manual, so the results should be the other way round. As I said, it really depends on your printer, so don't eliminate a process until you have seen the print.