I've been hand embroidering the 50 state bird and flower blocks. The transfers are so vintage that the states are written as "Mass." and "Minn." from before the MA and MN, etc, were adopted, LOL. My sister's godmother made her this quilt in the 60's, when she was about 12, and it was always the object of my envy! So I found the transfers were still available and bought them... I have 22 left to embroider but I find it so much fun and relaxing.
I used a good quality muslin to iron the transfer lines onto. Then if I have a long run of thread on the back, I weave it though the backs of other stitches so it won't show up as a single dark thread. On white batting I don't expect any thread on the back to show through.
You don't want to have anything too thick to stitch through, or it will become a real chore to get the needle and thread through it.