Here is a good tutorial for putting fabric appliques on t-shirts (well, onesies, but it's the same idea!):
http://www.michaelmillerfabrics.com/Blog/applique_onesie.pdfFusible webbing should work fine for something like a t-shirt. It will also reinforce the fabric and protect a bit from fraying. If you're sewing around an applique that's been fused to a stretch knit, it may also help to put a stabilizer sheet or piece of lightweight paper underneather while you're sewing. You can then tear it away when you're done.