I think I figured out why I was struggling so much! I want to do something that "brands" the teen area (and possibly even repels other age groups, but in a subtle way), but every time I pick something wild, I feel uncomfortable, because (here's the revelation): the library is one big room, and in order to look nice, I think it has to be kind of matchy.
Most of my library is brown and gray-blue. And by brown, I mean various shades of wood. So picking lime green rolly chairs and chrome tables would be jarring. And I decided I don't want the library to jar. I want it to gell. Ah, I can never resist an alliteration.
So my new idea is wooden benches and storage cubes with checkers and chess. I'm thinking clean and modern, geometrical, matchy, hopefully durable, and they can accommodate lots of seating arrangements. In fact, there is no wrong way to sit on them. The color scheme has splashes of brights, but mostly wood (and a little chrome).