I recently started using straight pins but I secure the pointy bits with pinmoores (or in my case disposable ear plugs). They are much faster to remove from the quilt than safety pins.
I have also used spray basting 505 and it worked quite well.
Make sure to baste sufficiently (I baste about palm-width apart). As for tacking the sandwich, I think you could treat it like Stitch in the Ditch. You can start at the edge of the center row and complete that row. Then move down one row. Like someone already said, the batting instructions will give you a recommended distance for quilting. If you stay within those guidelines, your quilt should be safe from shifting.
If you were to tie the quilt by hand, I'd say it doesn't matter where you start. The ties are not connected so there would be no pulling or shifting in the process.