Here's a pattern for rectangles.It's called flannel bricks.

bkay

You could also cut them in half lengthwise making 2 1/2" x 7" strips. Cut those in half and you have rectangles for "coin" or "zipper" quilts. So many possibilities!

took me forever to find this picture but you could add strips to the them to make them square. i think mine were 4x6. i added 1 1/2 inch strips on the 4 inch sides. then all you do is turn every other one on it's side. one up, one on it's side. looks like it was difficult but very easy.

I should add i put a navy border on so the sashings blend (even though they had tiny hearts). i was using my stash. somewhere i have a better photo.

i love disappearing 9 patch! i love to do it when i've got lots of squares laying around!

https://www.youtube.com/watch?v=dEjZOXxPazg

Ooh, I like Quiltwoman's suggestion. Since you say your fabric is all rather light, the dark sashing might give it more "pop". If my math is right, one yard would be enough for both quilts. I made a quilt similar to this, and it was nice because the dark strips visually hide places where my corners didn't match.

Bkay's brick pattern is what I was going to suggest. It will require minimal cutting (just cutting some rectangles in half for some edges), and also has the advantage that the corners are staggered, so if it doesn't line up perfectly it won't be visible in the final product.

Both these patterns are very doable as a first quilt. You could even do one of each!

Personally I enjoy working with something else besides squares all the time. There are so many pattern for rectangles. Have you looked on Pinterest for rectangle quilts to get an idea of what to make? Julienm1 suggested the zipper quilt from Missouri Star...I've made it for my granddaughter. So easy!

Suggesting “Meet in the Middle”. It calls for jelly roll strips sewed together on the 2.5” side but I’ve used 5.5 inch instead for charity quilts.

I love rectangles! And heartily endorse the idea of the “brickwork” patterns that LAF2019, Tartan, and others described.

Definitely, making one quilt in checks and the other in florals and solids like you mentioned would work.

A few more ideas to play with:
-- Make one quilt as scrappy as possible, and use the same fabrics in a very ordered layout on the other quilt.
-- Maybe use prints you have the most of (checks and solid blue, it sounds like) to create a distinct pattern for each quilt that draws the eye, and mix in the other fabrics as needed. The main pattern could be horizontal, vertical, stair-step, or even (roughly) circular to expand out from the center.
-- Cut the blue solid rectangles into squares and use them to separate/break rows or columns of bricks.
-- Select one of the prints and stitch them all end-to-end to create a one-print "solid" fabric that goes between rows/columns of mixed bricks.

Hope this is helpful. We'll want to see photos of what you come up with!

Look at the book, East Meets West quilts. There are quilt ideas using rectangles pieced into blocks in different proportions.