Dear Confused,
The best quality fabric is the one you can afford!
I have NEVER checked for thread count on a fabric. But I do check for the 'hand' of a fabric - does it feel right to me? Lots of others will explain what the 'hand' means, my brain just turned that thought off!
Having said that, I have been able to find good quality fabric and not so good quality fabric in every quilt shop I've ever entered - even the chains.
I frequently use both 100% cotton and poly/cotton blend sheets for backing and have had no problem with that - so far. However, if you plan to hand quilt, a sheet might be difficult to use.
Good luck and have fun!