I am in the middle of a big memory quilts project myself, and I put interfacing just about everything - except bluejeans. I used Pellon Featherweight... but this is my first time using interfacing so I am far from an expert. But I can tell you that after I ironed on the interfacing the tshirts are actually more "soft and cuddly" because they have some body to them.. they did not get stiff in anyway. My seams did not get bulky at all
I interfaced before I cut my squares and I am glad that I did... because as others have said the curling of the edges on the tshirts.
Good luck.. I am sure your quilt will turn out great!