So there's absolutely nothing in place at all at this stage?
There's plenty of places around that do all this kind of stuff. I'd suggest going somewhere that does all sort of merch, stubby holders, caps, all sorts of crap. So if it works out and the merch expands, it can all stay at the one place.
I guess if there's no-one on here that has an actual contact to get the printing done, the first step is to work out the numbers of the initial print, go to a few different companies and tell them what the go is and that it is potentially a long term on-going account, and get some samples done. Compare the samples and then go with the company that offers the best deal/quality/lead time.
If they have the hardware (t-shirts, caps, etc) in-house at the printers, that eliminates the headache of sourcing those things first. May be more expensive to set it up that way though.