I back baste, and while basting I pin from the "back" side so my thread never catches on it.
As for the background fabric staying flat, a few things...
1. Try not to hold your piece high up in the air while stitching. I do best if I lean on the arm of my sofa or chair and let the arm support the fabric, too.
2. Don't clench your fingers too tightly around the fabric, even when you're irritated
3. Flatten the piece every so often to make sure everything is still where it should be. Make a correction right away if necessary.
4. If your fingers are wet or sweating, stop and dry
I hope this helps!