I don't know any 'correct' way to quilt except what works best for me. Usually the first thing I do is stitch the top edge, though I've been known to SID the inner part of the border then the top edge. At least this holds the border firm to quilt it, then everything else follows on, depending on the design on the quilt. Sometimes I do from top to bottom, then remove and reload to do the side borders - then again, the one I'm on at the moment am quilting the side borders bit by bit as I go. You have to have exact measurements and space each design evenly if you go this way.
The only issue I feel, is if you quilt, say a 5" E2E pattern left to right each row, it could push the batting and the top, to the right, so with smaller designs I will do right to left each alternate row.
Just do what seems right to you.