You can minimize the curl somewhat by using a fairly deep garter stitch or seed stitch border. Both lie flat but may “flip” because of the tendency of stockinette to curl.
If you decide to use a garter stitch border, you’ll need to periodically add an extra row of garter stitch in the border. This is because, row for row, garter stitch rows are shorter than stockinetee or reverse stockinette.
I like the German twisted cast on for stretch and Jeny’s amazingly stretchy bind off but it’s a matter of personal preference.