My first piece of advice would be to NOT cut anything until you know what your block size will be. You may need to have a lot of background around a picture, etc but it is way easier than working with many different size blocks. For a first time t-shirt quilt I would try to have all my blocks be the same size.
I would definitely use stabilizer. And be sure to iron the stabilizer on before you cut your blocks out. You want the stabilizer to go all the way to the edges of the blocks so that you don't end up with blocks that are out of square.
Here is a pic of the modified one I made my daughter for her fifth grade graduation gift. It included t-shirts and hoodies from K3 to fifth grades. The hoodies all have open pockets and the one in the center has a working zipper with a tie die t-shirt that is visible when it is unzipped. It was crazy because of all the different sizes but it turned out great!
There are some super tutorials online. Just google t-shirt quilts.
