When to start Language School studies?

I know that April is standard month for most of the new studies/fresh jobs startings but I see that major schools often allow to choose from 4 different months (Sep, Nov, Jan and Apr). What would be the most appropriate for me considering I am aiming at getting EJU/JLPT2 and applying to Uni? I have checked Uni pages and most of them require to provide documentation and take exams in Spring (which gives me anxiety considering I can take JLPT/EJU only twice a year and after only 1 year of studies in JLS (out of 2-year programme) I might not yet be able to accomplish that. Therefore it seems logical to start at JLS in September but I still have doubts. On some Uni pages it is written that foreign nationals are allowed (or required?) to take exams during Autumn, that makes things even more unclear for me.