I have made well over a hundred burp cloths (for kids and friends of kids who were having children). Mine are roughly fat quarter sizes and made of 2 pieces of flannel with rounded corners. When shopping for flannel I do a lot of feeling as I have found that some of the stiffer feeling flannels never soften up. I buy fat quarters or no more than 1/2 yard of the flannel and wash and dry it (I buy the flannel anywhere I find it -- LQS, Joanns, etc). Once I wash it I feel it and only use the softest. Flannel shrinks when washed -- and no 2 pieces even from the same manufacturer shrink the same. I have also had flannel become threadbare -- both LQS and others. After washing, I pick the softest pieces for the burp cloths because (I have been told) they make great snot rags as the little ones get older. The rejects go into scrappy backs.
I have never used baby terry cloth -- sorry.