Lovely colours, you have enough colour and patterned fabric in the blocks, therefore I would go with a cream (neutral) this will "Frame" the blocks and really show them off.

My first thought and last is a blue white. Perhaps a plaid in the boarder. very pretty.

So this will not need quilting when you are done, is that right? I like the color combinations and should be very pretty. I would say a light blue would be pretty.

I like the rose colored sashing idea. I would also entertain hot pink and other pinks. It is a very pretty quilt. Thanks for sharing.

Don't you just love string blocks? Over at Quiltville we just finished a mystery with string blocks - ours were 8 1/2" then sliced in half at the triangle end and these two and two more sliced string blocks were added to make the main block - it is gorgeous - the fabric really moves.
As to color, I would add a gorgeous pop in color - maybe a darker blue??? Batik maybe?
Judi in Ohio

I agree - you need something darker, but narrow strips.

I would definitely go with a darker blue to make those beautiful squares pop.

White or cream. But I think the white would be more WOW with those beautiful fabrics

Light blue or white. It is going to be pretty.

I'm thinking a pale blue would coordinate and not take away from your beautiful colors in the block.