I almost never rip out and start over, but this is a situation where I would do it.
Once you have the quilt layers apart, I ***strongly*** recommend heavily starching the backing. I use a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" this onto the backing using a large wall painting brush (kitchen island works great for this task), wait a couple of minutes to make sure the fibers have had time to absorb the starch, toss in dryer, and iron with steam. This stabilizes the fabric so it is much less likely to stretch, distort, or pucker while you machine quilt.
I also recommend that you spray starch the top before layering. Spray starching is not quite as strong as the above method, but works better with a top.
Spray basting keeps the layers together better than pin basting. This is because the basting spray keeps all 3 layers in continuous contact with one another. With pins, the layers are in contact only where the pins are.
What kind and brand of batting are you using? Polyester is more slippery than cotton, and there is more of a tendency for layers to slip and slide with polyester. Spray basting also has fewer problems when you are using cotton batting.
My recommendation for basting spray is 505; it tends to work well even on polyester batting. Another possibility for you would be glue basting with Elmer's. There are tutorials here on the QB about how to glue baste a quilt.
Depending on your pattern, quilting diagonal lines may mean that you are quilting primarily on the bias (especially for the backing, but also may be the top). The bias of fabrics stretches more easily than either the straight or cross-grain. Although it's certainly possible to quilt diagonal lines on a quilt, as a beginner you may find it easier to quilt crosswise or lengthwise lines. In any case, spray or glue basting plus starching will help eliminate the problems you ran into.