Screen Printing
Pros: Can deliver high volume. Multiple Colors.
Cons: Equipment cost - Screens, Stations, Dryers, Emulsion equipment, software. Time to learn emulsions, separations, squeegee techniques. Labor intensive, (sweat.) Difficult to do fine details. Low volume impractical/not economical. Larger space requirements.
Sublimation
Pros: Photographic like output. Comparatively cheap, (varies, some printers are out there on price.) Great hand. Suited for low runs, (even one or two.) Smaller space required. Can sublimate things other than shirts such as ceramic or aluminum.
Cons: Polyester only for tees. Harder to do high volume. No white ink.
Vinyl
Pros: Material costs are low. For a bit more, unique materials, (glitter, metallic, ect.) Glitter and metal and other materials can be high demand. I have seen glitter screen printing ink though. Good for low runs and or high customization. Cutter can be used for other endeavors, (signs, decals, rhinestones, ect.)
Cons: Poor hand, (varies with material). Impractical for large runs or high volume. Must learn vector graphics. Nothing near photo output.
As you already have a cutter, like Wild Goose suggested, why not grab a press and branch from there? Your half way there already. You didn't mention DTG, which is very high cost, and has it's own pitfalls nor did you mention Laser transfers, which require a press and a laser printer known to work with the transfer material. Outputting white ink in Lasers cranks up the cost. There are also transfer solutions with solvent or eco-solvent print cut solutions such as the Roland BN-20, ($8500 + supplies.) There are lower cost inkjet solutions, that can work in a print cut workflow, but most find those something of a kludge.