The presumption right now in the hobby is that all Neocaridina species interbreed with each other. That means the following are NOT COMPATIBLE:
Yellow Shrimp (Neocaridina heteropoda var. yellow)
Snowball Shrimp (Neocaridina zhangjiajiensis var. white)
Blue Pearl Shrimp (Neocaridina zhangjiajiensis var. blue)
Wild Neocaridina sp.
Wild Neocaridina zhangjiajiensis
Green Neocaridina sp. (goes by various names, usually "Green Shrimp" or "Neon Green Shrimp")
Among the shrimps that would not pose problems from an interbreeding standpoint:
any of the Bee shrimp family (CRS, Bee, Golden Bee, Bumblebee) (Caridina cantonensis)
any of the Tiger shrimp family (Tiger, Super Tiger, Blue Tiger, Red Tiger) (Caridina cantonensis)
Amano Shrimp (Caridina japonica)
Dark Green Shrimp
Sri Lankan Dwarf Shrimp (Caridina simoni simoni)
Indian Whitebanded Shrimp
Red Nose (Rudolph) Shrimp (Caridina gracilirostris)
Which you chose will depend a lot upon your water; if your water is on the alkaline side (which is what RCS prefer), then the ones in the list above most likely to do well are Amano, Malaya, Dark Green, Sri Lankan, Indian Whitebanded, and Red Nose. If your water is on the acidic side (not good for the RCS long-term), then you'd want to choose from the Bee or Tiger shrimp options.