Good invert(s) for a 20gal. Betta tank.

mystery snails,cheap and redily availible.. cherry or ghost shrimp,also readily available

Just make sure there are lots of hiding places and cover because some Bettas enjoy eating inverts. My older boy doesn't even like snails.

Bettas can be hit or miss with inverts. They often will try to eat baby shrimp but with enough cover this is not a huge issue, especially in a 20g tank. They are good scavengers and quite fun to watch. Snails can be iffy as well with bettas as the bettas can often take a liking ot nipping their antennae. Again, it depends on the personality of the betta and I think in a 20g planted tank its most likely it would be fine. I would recommend a pomacea bridgesii ("mystery" snail or apple snail). They are not efficient algae eaters and do need a specific diet of calcium rich foods in order to remain healthy (veggies are easy).

My betta shares his tank with a pond snail (came in as a hitchhiker on some plants) and doesn't seem to bother him. I've wanted to try some ghost shrimp or pygmy cories, but you never know what will bring out his tiny inner predator.

bettas can be nippy towards snails, but that just depends on temprement. my betta hasnt ever tried to nipp and snails i have, but he is realy chilled out.

shrimp and snails would work good and very fasinating to watch. just make sure theres plenty of cover for the shrimps.