Oh hey, is that one of the SSB watches? I have one - the pushers for the chronograph are really satisfying. I'd love to see them do one with a 30 minute subdial instead of 60. It's cool that they're available with interesting dials.
I do also have a mechanical watch. Might get it a display caseback...
It really comes down to what you want. It's really hard to make an objective argument for a mechanical watch but it's cool that something with a balance wheel to regulate the timing can be so accurate. (All but the cheapest quartz watches are better, but still.) Generally enthusiasts are more interested in mechanical. The watches I own to do jobs are all quartz though. One's even a smartwatch.
Citizen Eco Drives are forgettable in a good way, available in a ton of styles, and mostly within your price.
The ones marketed as women's are pretty small. It's a classic feminine look, totally valid.
You also see women wearing unisex watches, about a 36 mm case. On a lot of women's wrists, it's the same proportions as a contemporary man's watch on a man's wrist. To my eye, it's a little more of a statement, "I have the right to vote and nobody cosigns my credit card." Also totally valid. (Side note, I have a 36 mm watch for my average-sized man's wrist, it looks a little small next to my other watches but it's extremely wearable and was the style for a long time, this is all made up anyway.)