T-shirt manufacturer? Got art for shirts

The trouble with T-shirts is I believe you can't reproduce too many colors and even the colors that are in the original artwork becomes "flat colorized "so to speak. That being said, I'd like to hear from a Ferrari fan who makes T-shirts to see if any of the original art I have is reproducable on a shirt. We could talk about use of the art for x-number of shirts.

Also seeking opinion on which side of the shirt to print. The artwork is rectangular so my idea is to print the image of the painting on the back of the shirt, leaving the front blank, using black shirts. only Also the purpose of the shirt is only to promote paintings not to sell the shirts so I'm thinking of handing them out free to svelte ladies I see at Ferrari events. Would the femmes prefer artwork on the front or the back? I'd ask my wife but she is long since aged out of competing with the youngins clothing wise. I myself only like shirts with collars but I think some t-shirts are collectable (at least in rock and roll circles)