Case size is one of the most important factors when selecting a watch.
These are general suggestions for different wrist sizes, to keep the look proportional to your wrist. Following this should result in a good aesthetic (not too small or too large) and tends to result in optimal comfort, regardless of your wrist size.

Case Diameter
5″ wrist circumference (recommended 30 mm to 38 mm diameter)
5.5″ wrist circumference (recommended 34 mm to 39 mm diameter)
6″ wrist circumference (recommended 35 mm to 40 mm diameter)
6.5″ wrist circumference (recommended 36 mm to 41 mm diameter)
7″ wrist circumference (recommended 38 mm to 43 mm diameter)
7.5″ wrist circumference (recommended 40 mm to 45 mm diameter)
8″ wrist circumference (recommended 42 mm to 46 mm diameter)

Case Thickness
Considering proportions, one area often overlooked by less particular watchmakers, is the case thickness. Watches 8 mm to 14 mm thick tend to wear best across the spectrum, meaning they look proportionally correct and fit well ergonomically.
Once you go over 14 mm, the watch tends to look like it’s bulging off your wrist and becomes harder to slide under a long-sleeved shirt cuff. Generally, a dress watch is far thinner than a sports watch.
Be careful because some unscrupulous watchmakers will list the thickness of the case and the watch crystal separately, whereas the industry standard is to list the total thickness of the case and crystal as one number.

Lug-to-Lug
Another factor to be aware of is the lug-to-lug length of a watch case because this number determines how the watch will lay on the top of your wrist. Too long of a lug-to-lug and the watch will hang over your wrist. This is generally undesirable, and almost guaranteed to be uncomfortable. I prefer watches that are 50 mm or less lug-to-lug and recommend not going much above that unless you have very large wrists, or if you don’t mind the lugs protruding beyond your wrist.

Lug Width
The lug width (or interlug width), is the width between the two lugs on each side of the case that determines the width of the connection point between the bracelet or strap and the case.
17 mm and below (very small)
18 mm (small)
19 mm (unusual size)
20 mm (most common size)
21 mm (unusual size)
22 mm (large)
24 mm and above (extra large)
From the lug width, a bracelet or strap either stays the same width down to the clasp/buckle, or the width tapers down. Non-tapered bracelets or straps tend to create an aggressive look like you see with a nylon Nato-style strap. Generally, tapered is preferred for a standard, elegant look.

Summary
Pay attention to a watch’s case diameter but don’t forget about thickness, lug-to-lug length, and lug width. Size does matter and choosing a watch that fits your particular wrist size well will enhance the overall appearance on your wrist, as well as the comfort.