T-shirts quilts became the bane of my quilting life when I started making them for others, post-retirement! I started first cutting the logos out of the shirts(front or back)with at least 4" extra (more if I'm doing multi-size blocks using pocket sized logos, etc).
I suggest you either use graph paper or a computer design program like EQ8 to plan a multi-size blocks quilts before you start cutting so you know how they will fit. If you have some pocket-sized logos you can sometimes applique them onto a related shirt. If you don't to bother with work of the multi-size blocks, try to find t-shirts that the logos are either same or multiples of your largest blocks (i.e. all 14" blocks. Or some 12" and some 6" blocks in same quilt)
2nd I apply the fuseable--favorite is Pellon ShapeFlex and 2nd is Pellon 911FF or similar. I then trim these down to the size that I plan to use to piece.
While piecing the blocks/sashings I work in either rows or columns to avoid Y seams.
Quilting is difficult when you have 2 layers of t-shirts and fuseables and batting to go through by hand or machine. If you do decide to use t-shirts on the back, I suggest you tie the quilt instead of either hand or machine quilting. Good luck--fun memoirs!