First rule, pre-wash everything the way the quilt may be washed, so there are no wrinkled seams from uneven shrinkage. Yes, different thicknesses will interfere with the quilting, and also with the ability of the quilt to withstand the wear of being used. Wool, for example, is usually less washable and more prone to fraying than cotton. Cotton blends and synthetic fabrics are also more likely to fray. T-shirt fabric works better with a very light-weight iron-on interfacing to stabilize it; then it should work okay with flannel or cotton. Batiks ARE cotton, and I've seen quilts with both quilter's prints and batiks mixed.
My suggestion is Keep It Simple to Start -- use good quality cottons only first. Then try a small project ( like a pillow top?) mixing two fabric types, quilting it, washing it, using it, and see if you are happy with you results.