My question is simply:
How could I pick next year’s classes and ensure that I get into them if I am transferring from another high school? In this case I would be moving to another district - even though they are in the same city - and would know the school I will be transferring to and the courses available there through an online course catalog.
Thank you for any insite you may have! 
I would contact one of the guidance counsellors over there and see how soon you can sign up for courses and what you need to do to sign up.