I have never heard of standard ink, inkjet htv. All the printable vinyl I am aware of uses solvent or eco-solvent ink. Those machines run 9k-200k. There are transfers for standard desktop inkjets. but are not vinyl. They are not great I find. Mileage varies. The cheapest entry into full color that still looks good is what Dakotagrafx said, sublimation. It just works on polyester. I would just get a dedicated sublimation printer if I did this, and not try to run sub inks through my daily printer.
Maybe look into ordering plastisol transfers for the shirts such as https://www.fmexpressions.com/landing/full-color-program/ among many.