Usually the media are BG11 (for fresh water), ASNIII (for marine water). The light should be, or very low or not continue (however low intensity). Agitate or not, depend by the strain, but in my experience is better do not agitate the cultures when they are near to start or just started their growing. The insufflation of air+CO2 could help, but it could also create some problem about the agitation. However I suggest you to start with very small volumes (50-100 ml). I usually start with 3 small flasks, hoping that, at least one, starts to grow well, but in many cases I used 5 or more flasks to be certain to obtain a result in a short time.

The cyanobacteria produce different types of spores. If you are interested in isolating filamentous cyanobacteria which produce spores (akinetes) then almost all filamentous, heterocystous forms differentiate akinetes generally during late phase of growth. Grow these forms in any specified medium suitable for the growth of that particular organism and keep under normal growth conditions. When the organism will enter stationary phase of growth it will differentiate akinetes.