you certainly can combine fabrics in quilts- there are wonderful quilts that contain fleece= cotton, batiks, wools, silks---everything and anything-
using t-shirt knits you need to use a fusable non-woven stablizer- to keep the pieces from stretching while working with them- it is inexpensive-available in pretty much any store that carries fashion fabrics (like joannes-hobby lobby---some lqs)
when combining different fabrics laundering is the only thing to really worry about.
t-shirt quilts are made with t=shirts and cottons all the time