I have sifted through the family of rares of all kinds, several times, and they keep coming out with new ones. So just when you start building on some, some juicy new one may come along and interrupt your progress. From your picture you have a whole bunch of decent ones and some poor ones. How do you figure the good from the bad?
What I do is look at ratings, which realize is just some peoples' opinions. You can get input from the in-game ratings, which may involve a few to many thousands of opinions. I also recommend ayumilove.net which has tons of info on pretty much every champ in the game, and not just for rares. Not everyone likes either of those methods. But until you can develop your own criteria for what you keep and build those are good starting points.
So first cut, I would take your roster and run them through those resources, and make a first cut at what you prefer to keep. There are uses for general purpose, and ones good for certain locations that are bad most everywhere else. Obviously you can't develop everything, even trying to make a faction team for each faction is a long process.
And there are a bunch of others sub-rare that can be useful, ones like armiger, monk, shieldguard, etc.
I wish you well with it. Staying focussed on ones you start with is important. It is easy for us to drop names for you, but learning to select your own seems more important.