I prefer
Catherine.
I know
Katherine is the traditional Greek version, but in English it should phonetically be
Catherine. In English, words with second letters A, O, or U should begin with C; while words with second letter E or I should begin with K.
Examples:
cat, not kat
keg, not ceg
kite, not cite
cot, not kot
cut, not kut
I'm all for proper phonetics. :D
I admit that
Kathryn is a bit of a GP. (If you're going to put in a Y, why not add a K as well?)
Catherine, however, is the "correct" English spelling.