quilting it on your home machine it may be awfully thick to manuver with 2 layers of fleece unless it is quite thin fleece? fleece does quilt nicely. it is necessary to baste or pin baste your sandwich well (like every 4" (if you lay your fist down on the quilt it should 'touch' basting all the way around) so it does not shift/stretch while man-handling it through your machine. also roll it from each side and start quilting in the middle working your way out in one direction, then when one side is done remove it, turn it and start again in the middle going in the new direction. i would recommend making a small (12" or so) sandwich with the 2 layers of fleece and cotton top and practice to see if you can do it with that bulk or if you need to use a lighter weight inside layer (on my fleece backed quilts i used a thin single sided flannel for the batting. it came out great, not too thick but still very warm and cozy. Try different combinations to see what you like best and what works well for you.
looking forward to pictures! :)