You can never go wrong with the simplest choice of a plain ring of gold or silver. It's a classic no matter the time period and you can always make an inscription on the inside to make it special. This was common in the renaissance like this one:
|17th Century, gold poetry ring|
Reads: A loving wife prolongeth life
A very common ring in the Medieval was the stirrup ring - named so because it looked like the stirrups used when riding. They're simple and elegant and with a single or no stone. Found from 1200 and throughout the rest of the Middle Ages.
There's also rings with floral print (12-1400) like this:
|11th Century - presumably|