Here a start for you to reasearch with basic info. My concern is mixing shrimp and a betta's as I think will eat the shrimp is they are too small. I never housed bettas so I don't know about there temperment, but I know fish think shrimp are a taste snack. SO go with the larger shrimps would be safer.
Red Cherry Shrimp - Neocaridina Denticulata Sinensis - Size: Up to 3/4" pH:6.3 - 8.2, Temp: 70-82, Origin: Taiwan
Amano Shrimp - Caridina Japonica - Size: up to 1.25", pH: 6-8, GH: 8, Temp: 7-28 C, Origin: Japan
Malaysian Rainbow Shrimp - Caridina sp. Rainbow - Size: up to 1" pH: 6.5+7.5, Temp: 20 to 25C Origin: India
Brazilian Yellow-Belly Grass Shrimp - Palaemon Pantanal - Size: up to 1.5" pH: 6.4 - 7.8, Temp: 48 to 89F can handle more extreme cooler temps as long as they are gradual, Origin: Brazil
Rudolph Red-Nosed Shrimp - Caridina gracilirostris - Size: up to 3/4" pH: versatile Temp: versatile Origin: India
Bumble Bee Shrimp - Caridina trifasciata - Size: 1/4 up to 3/4" pH: versatile Temp: versatile Origin: Japan
White Spotted Pearl Shrimp - Macrobrachium mirabile - Size: 1/2 to 2" pH: versatile Temp: versatile Origin: India
Dwarf Blackberry Shrimp - Caridina sp. - Size: 1/4" to 3/4" pH: versatile Temp: versatile Origin: Thailand
Dwarf Emerald Green Deora Shrimp - Caridina sp. - Size: 1/4" to 3/4" pH: versatile Temp: versatile Origin: Thailand
Orange Halo Shrimp - Caridina sp - Size: 1/4" to 3/4" pH: versatile Temp: versatile Origin: Thailand
Black Forest Shrimp - Caridina sp - Size: 1/4" to 1" pH: versatile Temp: versatile Origin: Thailand
Singapore Wood Shrimp - Atyopsis moluccensis - Size: Up to 4", pH: 6.5 - 7.4, Temp: 72-85, Origin: Singapore