Welcome from Indiana!
I agree with the PRESSING recommendation. I think a thicker/denser polyester batting will help hide some of those imperfections.
Are the fabrics made up the same? 100% cotton; 80/20; 50/50 poly/cotton? Permanent Press versus 100% cotton? That could make a difference.
You state that you're 'new' at quilting. Are your seams consistent? 1/4" (or whatever you used). If some of stitching is done at 1/4" and then goes up to 1/2" and back down to 1/4" (visualize a wave) . . . that will definitely make for a wavy quilt.
Post some pictures if you have time.
Nan