Traditionally there have been men's, women's and unisex watches, but it's really just a matter of size, and sizes are a changing fashion. Of course there's styles that may be considered more masculine or more feminine, with women's watches traditionally emphasizing the jewelry aspect and men's watches emphasizing function, but there's plenty of overlap there. Just as in clothing, women generally have had more latitude in wearing "masculine" styles than men have had in wearing "feminine" styles, but that's changing these days, too, and there are plenty of examples from history of "men's" watches with floral designs engraved on the case, or gems set in the bezel, or whatnot, and many "women's" watches with tough, utilitarian, oractical designs. Lately, some brands are dispensing with gendered descriptors altogether and grouping collections by small, mid , and large sizes.
So, really there's only one rule: wear what you like and what fits you well, in both size and style.
Size trends currently are headed towards smaller watches after a couple decades of big watches being in fashion. There are a few measurements that sum up a watch and will give you an idea how it may fit, but just like clothing, the numbers don't always catch all the details and aren't a full replacement for trying it on.
The first will be case diameter/width. A pretty typical size for "large", traditionally men's watch is 40mm, but 38mm and 36mm are coming back into style. 33-34 is a typical mid-sized watch, and 28-31 mm for a small. These are typical sizes for round cases, square, rectangular, cushion, or tonneau cases "wear large" taking up more visual space for the same width, so they tend to be narrower. For example, if you look at one of the classic watch brands that has long produced both rectangular and round cased watches, Jaeger-LeCoultre, their traditionally fitting large round cased watches, the Master Control series, are 38-40mm wide, while their large rectangular cased watch, the Reverso, ranges from 28 to 30mm.
The next important measurement is lug to lug. This is the length from where the strap/bracelet connects on one side to where it connects on the other. This can be very variable and affect the overall fit as much or more than the diameter/width. Some makes are famous for "long lugs", like Nomos, which, despite their typical smallish diameters, will fit a large wrist well or, conversely, a small wrist poorly, because of the large lug to lug size.
Finally there's thickness. This is caseback to the highest point of the crystal thickness. Sport or utilitarian watches generally get away with being a bit on the thick side, emphasizing durability, weather resistance, or added functions, while dressier watches will work best if thinner, more discreet, and able to fit under your shirt cuff without binding. Diameter also comes into play here, since a 36mm watch that's 13mm thick will seem a lot thicker than a 42mm watch that's 13mm thick, simply due to proportions.
Then there's technology. Quartz remains a highly accurate, and generally lower cost, technology, but there's a world of difference between low cost quartz and high quality quartz. Quartz is often seen as "soulless" simply because it works, with no fuss, and little need for interaction, while mechanical watches have a fair amount of "care and feeding" instructions that come with them. Plus mechanical comes with a rich and interesting history, and often a transparent caseback, known as a "display" or "exhibition" back, which gives you a view of the visibly energetic work going on inside, which is always fun.
Basically, mechanical watches are not just time telling devices, they're also sort of a Tamagotchi, the "virtual pet" toys that were popular in the 90s that required interaction to keep them "alive".
Within the realm of mechanical watches, there's manual and automatic watches, with a manual (sometimes referred to as just "mechanical") requiring regular winding by hand to add power to the mainspring, while automatics use an autowind device, a rotating mass (the "rotor") and gearing to harvest energy from normal arm movement and store it in the mainspring. There are positives to be said for both. I enjoy a nice manual since wearing one let's me start the day with a few tens of seconds spent winding it until it's full, meaning I get to check an item off my "to do" list without even getting out of bed. Plus, they tend to be thinner since the addition of the autowind device adds to the bulk of the movement. But, there are some very thin autos out there. On the plus side for autos, you have the added complexity of the device, which can add appeal for a gearhead, plus the convenience of not having to wind it up every day. And, with the vast majority of autos, you can wind them by hand if you want, adding extra power. This is useful if you're a relatively sedentary person, since if you're not active, it won't be able to harvest enough energy to keep running.
Mesh bracelets, also called Milanese bracelets since this method of interlocking wire coils to form a flexible mesh originated in the city of Milan, are a great choice, and one of my favorite bracelet styles. But, quality really matters for Milanese bracelets, and with heavier watches you want a thicker mesh to give some mass to the bracelet to act as a counterweight, keeping your watch nicely centered and located on your wrist without having to wear the bracelet too tight. A well-balanced and well-fitting mesh bracelet is very comfortable.
Mesh bracelets, owing to their straight ends, can usually be fitted to most watches, and there are a few makers of Milanese bracelets which excellent bracelets, with good adjustability, so if a watch is not offered with a mesh bracelet as original equipment, it's usually easy to add one. My favorite mesh bands are the German made Staib bracelets. They're very supple, nicely finished, and just all around solidly made.
So, that's some basics.
Very cool. That's an interesting and good looking dial.