Cute suit! To me this looks like a double knit with a decorative added stitch on the face. Double knit can be patterned with designs. You'd also need to know the fiber, which is hard to tell from looking. So it would be a [fiber name] double knit. If there is any thread to cut and try burning, here's the instructions for how to determine the fiber:
https://vintagefashionguild.org/determining-fiber/
Built-in bra is actually the proper term!
Size is usually a matter of measuring the suit as best you can. There was a discussion of this quite a few years back here:
https://forums.vintagefashionguild.org/threads/how-do-you-measure-vintage-swimwear.13743/
Two very important measurements that are sometimes left out: Top of the strap to center crotch length, and measure the bra part by following the inner contours at the center (where it's fullest).
