I am new to quilting, but picking out colors and fabric is my favorite part. I think of who the quilt is for? Where is it going to be used or displayed? Does the room have a color theme? Does the recipient have a favorite color? And then go from there. For the square within a square, I would probably choose a nice floral fabric or other focus fabric (butterflies, kid's print or whatever depending on the purpose of the quilt), then you can either choose two or four tone-on-tone fabrics with colors that go with the focus fabric colors for the setting triangles. If you want a scrappy look, you can go with any number of colors for the setting triangles and arrange the blocks randomly.
Also you can do a search on the board or the internet in general and take a look at how other quilters used this block.
Good luck and have fun.