Hi, I just made a quilt called head over heels and it was all kinds of shoes, I used fleece for the backing, without any batting and it came out really nice.
I did a stippling quilting on it and it was really easy to do, I did use a spray first and that kept everything together,
I think your t shirt quilt would be fine using fleece without batting, the t shirts make a heavy quilt so I don't think I would use batting,, Good luck and post a picture when your done