Cross-hatching would work well, as would the echo quilting mentioned above. Two things to remember are that your stitches will practically disappear into the quilt, especially after it is washed, because the T-shirt material is so squishy - and therefore any slight errors you may happen to make will be virtually undetectable - and that you DO NOT want to quilt over the plastic/paint/latex that makes up the logo or design, as this will gum up your needle, give you weird uneven stitches, break your thread and generally make you wish you hadn't tried it. (Ask me how I know.)
Tiresome to you as it is now, I am sure that the finished quilt will give great joy to the person receiving it!
Alison