I tend to not make 'baby' quilts per se, but more 'toddler' quilts. I've done muted but I've also done (and tend toward) more vibrant colors. I also like the idea of red; white; black for a baby quilt.
A quilt that I did for an older niece was a mixture of HST's and plain (background fabric) squares and set as a 'kite tail' flying through the air. I had particular color requests for that one but you could do any combos with that kind of pattern since you said you were looking for geometric shapes. Just a matter of spinning the HST's around to get the 'kite tail' movement.
Personally I'm not a fan of mixing white with beige but that's me. I've also done very pastel. The background on the latest was a white/grey combo and I picked other fabrics that had a bit of that along with pinks and greens as it was definitely for a girl. Very soft looking.