Ava is a little bit faddish, but also classic. I guess it's classic-faddish (like Emma and Grace, etc.)
I love Eva! I pronounce it AY-va, although I also like EE-va. I think it looks a little nicer and is less faddish and less likely to become dated/trendy.
I don't like Katharine. I like Katherine, but I'd still say Eva is way better than Katherine.
Genevieve Katharine isn't bad. It's a bit diva-ish but not in an OTT way. I'd prefer just Eva "Eve/"Evie" or Eve "Evie" though.