I don't think there is one single best (or worst) brand.
One thing you will want to look for is the quality of the printing (unroll a yard, and check it for flaws or irregularities in the print). How many colors are in the design? (See how many color dots are along the edge.) More colors means a greater depth and richness to the design.
Touch the fabric; run your hand across it to feel if it is rougher or smoother. The way a fabric feels is very important to most people! Some of the inexpensive fabrics in the chain stores are definitely rough or stiff; these are fine for crafting and charity projects but you might not want them for a heirloom quilt for your family, or for clothing.
And while you're touching that fabric, if it's a dark color see if the dye rubs off on your fingertips. (That is a bad sign.)
Some fabrics are thicker/beefier than others. You will probably develop your own preference.
All the above details you can determine before buying. But as to whether a fabric will shrink badly or lose color/run in the wash, you won't find out until AFTER you've purchased it. So it would be a good idea to get yourself a little notebook, and if you run across fabrics that misbehave, write yourself a note to not purchase that kind again.
My own preferences:
Softest to the touch: Studio E (they mainly do prints) and RJR's Cotton Supreme solids
Beefiest fabric: Michael Miller, Timeless Treasures, and Robert Kaufman have been very consistent through the years.
Excellent printing of intricate designs: Elizabeth's Studio
Best metallic prints (if you like the sparkle): Blank Quilting, Hoffman, Robert Kaufman
Of the chain-store brands, I think VIP/Cranston is the best.