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The most common compost worms are the tiger worms, such as the species Eisenia foetida, and the red wrigglers
(Eisenia Andrei). In the case of E. foetida or Californian worm this has the advantage of having a high rate of conversion (1:1 from matter organic to compost) wide range of tolerance, supporting temperatures from 18 to 25˚C, a pH from 5 to 8.4 and also is fast breeding (in three months you can duplicate the population within 80% humidity and 20˚C). The species is easy to find and is often used as fishing bait. The type of culture can be a mono or multi species and according to my experience the best option is to have a mix of them due to environmental changes which naturally occur in your culture.
Wormfarming Blog 