Oh my goodness, what a marvelous little treasure trove! It sounds like you don't have a sentimental attachment to particular ring, so...if I were in your position I'd look for the pieces I'd be most comfortable wearing - even if only on an occasional basis - and the highest quality pieces. For me, that would be the two big stones in the first row (OK, I'll admit some bias because Amethyst is my birthstone); the emerald cluster ring in the third row, and possibly the ruby band-style ring in the fourth row or blue cluster ring in the bottom row. (The pink and yellow ring in the second row is interesting too, but I know from experience I'd never wear that particular color combination.)
One thing to look for is metal purity markings on the rings. In the 60's - 70's there was a lot of 10K jewelry sold in neighborhood pharmacies and gift shops. These pieces were generally made with lesser quality genuine stones, or synthetic colored stones (spinels) with very small "diamond accents".
The stone in the asymmetrical ring next to the ruby (?) band ring is intriguing. I'm wondering if it's an alexandrite. Does it change colors in different kinds of light by any chance - i.e., natural light vs. incandescent vs. fluroescent? An alexandrite would change from teal to purple, or some variation of that... and they're notoriously hard to photograph. There are both natural and man-made alexandrites, btw, and have been for many decades.