I have had bad luck quilting across the printed designs on T-shirts (the kind that you can feel a change in texture) - my tension goes wonky, and frequently the thread frays and snaps. This may be something I am doing wrong, or something to do with the thread I am using, but I now avoid sewing over the design if at all possible (and grit my teeth to avoid cussing when I stray over the edge). I often do little isolated spots of quilting in "blank" areas inside the pattern (where the original T-shirt color has been used as part of the design) - not very geometric, but it helps to accentuate the pattern of the T, and it holds the quilt together.
Because T fabric is so thick, a fair amount of your stitches will bury into it, which is nice if you are using a contrasting bobbin thread that pops through at all - you don't notice it as much. I tend to change thread color with each new shirt color (but keep the bobbin thread the same), but this is definitely a personal choice - do what feels/looks right for you!
Alison