Does the color of the shirt matter?
I think I have a shirt in mind that COULD work, but to give you an idea, a
white t-shirt, s/s, no pocket WHOLESALE can run on average $1.15 each, the same shirt in COLOR can come close to $2.00 each, so WITH a pocket and LONG SLEEVE you're really asking for a lot! :)
... I'm not saying miracles don't happen, but if you (can) drop the pocket requirement we might be able to help you out.
How many t-shirts were you thinking you might need?