I love
Katherine and
Catherine and even
Katharine but I dislike
Kathryn. It just looks...lacking.
I'd assume the spelling
Katherine but I would probably ask someone how they spelled their name, because there are so many spellings.
I think
Katherine definitely works as a full name, and while I love many of the nicknames the full name is so lovely.
I've met a handful of Katherine/Catherine's in my life. But definitely no more then five. Keep in mind however that I grew up in a largely Jewish community and
Katherine is very uncommon among Jews (it's still one of my favorite names though).