Generally chlamy can grow in almost any freshwater growth medium, it is not a picky species. Since it is easy to prepare, I can recommend BBM. Otherwise any medium that is used in your lab should be fine. If you want it to grow fast after isolation, you can add organic carbon, but beware that you are then also feeding any bacteria that might be present in your culture. Hope that helps! Best, bastian
I would suggest a freshwater simulating medium, for instance the Bold's Basal Medium. It doesn't contains carbon sources, so you will have to provide it through air bubbling or through inorganic salts addition (see my paper "Cultivation of Chlorella vulgaris in tubular photobioreactors: A lipid source for biodiesel production", Frumento et al., 2013). You will also need to adjust the temperature conditions depending on the strain type (equatorial, boreal, snowy, etc.).
For Chlamydomonas species Tris Acetate Phosphate (TAP) medium is the best as I have experienced. But because of the acetate content the culture must be axenic.