I suggest you use a lightweight fusible interfacing. There are some woven ones out there that are nice to use for it. Iron the interfacing on before you cut the T-shirt to the block size. The interfacing will help to stabilize the knit material and help reduce stretching.
As dakotamaid said, there are a lot of interesting settings and inspirational quilts if you do a search for T-shirt quilts on here.
One of my friends made a T-shirt quilt and she didn't have enough T-shirts to fill the number of blocks that she needed. So, she cut the backs of the T-shirts apart and sewed them together like a crazy quilt block and used them as filler squares.