I do not buy precuts. I buy yardage and cut my own pieces. I always wash fabrics when I bring them home. I fold them using a 6" x 24" ruler. To cut fabrics with a ruler, you will need a large mat, rotary cutter, extra blades and know to keep fingers away from the edge. You tube should have directions for using rulers.
All fabrics ravel along a cut edge. Quality really doesn't have anything to do with it. Same for fabrics that bleed dye. Some colors are more likely to bleed than others. I would find medium quality fabric for a few quilts. Top quality fabrics can cost quite a bit.
It will take lots of time to learn all you want to know and learn to do. Remember practice - practice and practice some more.