I'd choose
Karina, simply because I love girly names that have short spunky nickname possibilities (I have a friend named
Karina who goes by
Kat, but then there's
Karrie or
Rina or whatnot).
My pronunciation of
Kara is hard to explain in writing (my middle name is
Cara, so it peeves me when people don't pronounce it my way). It's not CARE-uh and not CAHR-uh. The A is the same is in apple. But most people would say KARE-uh.
I've never really seen
Karen as dated. It still hasn't left the top 200. I have seen
Kara as 80s either. I much prefer the C spelling though, but that might be partially due to bias. The only Cara/Kara s I have ever met have been born in the 90s or 2000s. And I don't see
Karina as cutesy.