I would do three lines of diagonal crosshatching, up the edges and middle of the "ladder" part.
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You will need to do more quilting inside the squares; you could use any curvy fill in there (meander, paisley, loops, etc), or you could quilt in a motif like a feathered wreath or a leaf or something. I would choose something that suits the recipient.
For the border you could do straight lines parallel to the edge, or gentle waves, or a meander or fill to match the squares.
I like the subtlety of the pattern with your colours. It feels very natural. Good luck with the quilting!