Welcome to classic wristwatch
There are few things a gentleman can wear as jewelery. A ring, a pair of cufflinks with a long sleeved shirt and a watch are about all that would be considered acceptable.
For a lady, early wrist watches were of very different design to those available today. They were smaller and more elegant, pieces of jewelery rather than simply a thing to give the time. Many of the Art Deco style cocktail watches that were so popular from the 1930s to the 1950s are of superb design. Any of these watches would grace the wrist of a discerning lady who chooses to wear one, and it would be noticed and commented on because of the unique design.
There is an enormous choice of modern watches, but there is nothing like the wearing a fine classic or vintage watch. Something made with real care and attention to detail, designed to the highest mechanical and aesthetic standards, and with some real history. These vintage watches are mechanical marvels made by highly skilled craftsmen. In the days before mobile phones, television, and all the other ways of knowing the time we now take for granted, they were relied upon to do the job, so had to be well made. The only other ways of knowing the time accurately was to wait for radio announcements on the hour, or to use the telephone service to obtain it.
The modern electronic wristwatch, including the so called 'smart watch', has little real value. A collection of programmed chips in an easily produced case, they are short term novelties that will become outdated by advances in technology very quickly. They are just another example of our modern society, where nothing is built to last and everything is designed to be thrown away the day it malfunctions or is replaced with an updated version.  
There are many different designs of vintage watch, and when the one that appeals is chosen and worn regularly, it will become like an old friend, and noticed by others because it is so unusual.
There were watches made to suit all sorts of specialist users in  those years gone by. Doctors watches with large second registers and pulsations dials. Sports watches, pilots watches, divers watches, nautical pieces. Understated dress designs to simply tell the time, or the time and the date, or the time, date, day and month (termed calendar watches). Chronographs for those who needed to time various events, including motor racing and many other sports. Pilots chronographs with slide rule bezels for making calculations. Watches for nautical use, and for divers, where the corrosive effect of salt water and damaging pressure had to be accounted for.
In the 1950s, the phase of the moon was considered to have an effect on all sorts of things. So it was not unusual to see a watch which could tell the moons phase. All but a plain watch are termed 'complications', and they are beautiful pieces to own and wear.
The fact that many of the big watch groups, who now own the names that were once individual watch manufacturers, are making and naming modern watches in homage to the great originals, proves how stylish they were. Why anybody would want a modern equivalent in place of the real thing, I do not understand. As an investment, a vintage watch will prove the wiser choice, providing it is regularly serviced and kept in nice condition.
The fact that a vintage watch is likely to, at least, keep the majority of its value, and many are increasing in value over time, is another good reason to invest in one. Or to form a collection, to give a choice when choosing one for that special night out, or as an investment for the future.
Vintage wristwatches were smaller than the giant lumps available new today. Less ostentatious in a time when showing off was not a part of everyday life. There are exceptions to this, but they were commonly around 35mm in size.
The choice of strap or bracelet is another question. Straps can be changed to alter the appearance of a watch. They come in a range of colours, finishes and materials. Bracelets are heavier. A strap can be a problem in very hot weather, as it can soak up sweat. A bracelet does not have that problem, but can be a little cold in winter weather, and is more permanent.
ABOUT CLASSIC AND VINTAGE WATCHES
The dimensions shown in the descriptions of each watch listed are measured as per the image.
If you wish to see how a watch will look when you are wearing it, I suggest cutting a silhouette out of flexible card and holding it on you wrist to see how it looks.