I had a few shrimp with my betta and corys... Let's just say HAD them...
Shrimps are great, but I'd stick to an invert tank if I were you.
I had my betta with tets for a while, that was a good mix, except the tets died because the filter system was too strong for them, and they kept getting stuck.
Also, I've never cycled my betta tanks, they are uber resilient.