I'm big on finding the best translations too when there's multiple out there.
Pevear and Volokhonsky as a team translate many Russian classics and I've really enjoyed what I've read that they did (I've read some of their translations of Bulgakov, Dostoevsky and Tolstoy). Some say they can be too exact and don't focus as much on the "flow" but I think it's a plus they try to be so exact. They are contemporary and have translated many of their books recently within the last decade or two.
If you're into ancient classics, I recommend Richard Lattimore. Not sure what all he's done, but I read his translations of Homer's "Iliad" and "Odyssey" and both were excellent. His translations are from around the 1960s or so. He focuses on close translation, simplicity, majesty of the language, the flow of poetry and the structure and does great at it.
Some say Lattimore's translations are older and can be more dense and less vibrant, but personally I think they're really fantastic. But if you're interested in ancient classics and want a translation more contemporary and modernly "readable", I've heard good things about Robert Fagles.
Hope that helps.
apple trees and honey bees and snow white turtle doves