If you are not used to wearing a watch, or anything on your wrists, then trying to wear a watch when you run might be a bit difficult to transition to at first. However, once you start wearing one you will soon learn that they are hard to live without! And long gone are the days when watches were used strictly to just keep time. Depending on what version and brand of watch you get, you can do everything from track the length, time, and distance of your run to logging your heart rate, calories burned, elevation gain or loss, and other informative metrics. There are even "smart watches" that can sync to your mobile devices, allowing you to keep up with emails, text messages, and phone calls!
If you simply want to know what time it and have a need for very basic timer and stop watch functions, then a very inexpensive watch from a drug store would suit you just fine. These watches range from $10 to about $35 for nicer versions, and tell you time and date, have a stopwatch setting for keeping time during your runs and workouts, and have an alarm feature. If you want a watch that can track your mileage and distance, you might want to start saving up your pennies to purchase a smart watch or GPS watch. If this is your need, I would suggest a smart watch because GPS watches will track all the metrics a smart watch can (i.e. mileage, distance, pace, calories burned, heart rate, and elevation, as well as syncing with your computer or laptop to give you data on these metrics) but do not have the communication functions or mp3 abilities that a smart watch has. However, if you do not think you want to deal with text messages or emails, and if you prefer to listen to music on your phone or mp3 device (or run without music altogether) then a GPS watch is a terrific option.
If you are concerned about fashion, there are many smart and GPS watches that have interchangeable wrist bands. You can match your wrist band to your outfit, and dress it up or keep it more casual and dress it down! Cheaper watches typically don't have this capability.