Shrinking will do nothing for your backups. Backups only back up used space, not empty space.

If you're going to shrink, do a once-off shrink, then rebuild all your indexes to fix what the shrink did to them. Shrinking a little every night is a really bad idea. You'll be causing massive index fragmentation every time, necessitating an index rebuild of every index every night.

What I would suggest is a once-off shrink, shrink the DB to about 10% free, then leave it.