I wanted size, like Diana. Specifically, being migraine-prone, I wanted no chinks in the armour, so something that sealed against my cheekbones and allowed peripheral vision while sealing the sides, with wide arms too.
I wanted muted tints for the lenses. I'd read grey and green are the easiest on the eye in terms of protection and least distorting too. So though I liked the look of the pinks and yellows, I passed when I tried them on. I also did NOT want my eyes to be easily visible in the glasses (privacy issues) so I wanted a darker rather than lighter tint --- which works great in tropical sun, but YMMV.
Like Diana, last time I chose, I got tortoiseshell because I wanted a little interest as well as versatility, minus any metallic bits (don't like the look, plus have metal allergy issues). This time around, I'm considering a little colour on the inside rim and inside the arms, for a change. And possibly a dark (near-black or brown till you get close) colour for the outside, or a little textural interest? Flat black bores me i'd want some outre shape if I got black.
Shapewise, with sunglasses at least I want brow coverage and top of cheekbone coverage, so I do like a frame that tilts up at the sides to prevent the potential droop of say the aviator style. Especially as I have a heavy jawline and jowls and double chin. I also wanted a high bridge (short nose here) and a heavier top line on the rim to balance my heavier jawline.
When checking frames, apart from looking in the mirror, I make sure to check against light for glare, against different colours for distortion, poke my head out of the brightly lit shop to see how it does in shady outdoor areas (am I blind?? can I read the sign across the street clearly), and test my peripheral vision. Also I my shake head vigorously to see if they'll fall off, but you already wear glasses and know what feels secure, I'm sure.