Ghost shrimp are good starters but you can find very unusual and rare (read: $50+) shrimp on AquaBids.
I have 2 ghost shrimp in with my betta Rossi, they keep the tank crystal clear. They eat letover betta food but since bettas are carnivores, I add in some tropical granules every few days but not to often so they don't get over fed. A lot of places say that a 10 gal is fine for 100-150 shrimp. No. I would start with only about 10 unless you get a species that is hard to breed, otherwise you WILL be over run.
They don't need a filter but they like large air stones like these http://www.petsolutions.com/C/Aquari...ir-Stones.aspx
Make sure they can climb on it some, they enjoy it a lot.
Any shrimp wants a planted tank, they contain tiny good bugs that break down plants for the babies to eat. Add some hiding spots like a half of a small flower pot or large rocks to play in. Duckweed looks nice in a shrimp tank, more so then other floaters in my opinion.
Some shrimp can live together, some can't, some eat specific things like bacteria from water, others eat algae.