Absolutely agree with the Java fern and Anubias. They require little care and no special lighting. I see my bettas rest on the broad leaves of my Anubias after they eat a good meal. It's really cool to see them chill out like that. My bettas also love the mosses. Christmas moss is one of my favorites. For your shrimp tank I'd also try to put some Marimo moss balls if you can find them. My lfs has shrimp tank with bunch of those marimo balls of different sizes and few other plants (all live of course). The shrimp crawl all over those balls and seem to love hanging out on them. Plus it looks really great design wise.Plants for the vase/jar thing? Lol
Erm I'd do with some Java Ferns if you can find them, maybe some crypts or Anubias nana.
They're all robust plants that can survive most tanks.
The first is java fern, the second is Anubias nana.