Hey HarryKeig, welcome to the forum!
Ghost Shrimp seem to have a 50/50 chance on surviving. I think it all depends on the Betta and if they'll tolerate the shrimp.
Sometimes bettas eat them and sometimes they'll live peacefully together. (Mine ate them the day after i added them!)
Unfortunately neon tetras are one of the top worst fin nippers and are quite fragile as well.
I'd suggest snails; I personally have a couple cobra guppies in with my betta, but they all coexist in a 20 gallon, so I'm not sure how they'd act together in your tank. (The more plants, etc. where they can hide, the less likely you'll have any trouble). I've heard others keep their bettas with zebra danios and ember tetras, though tetras feel safer in larger groups which might not be best for your tank size.