Options to Change J1 to F1

Hello,

I have been in US for 9 months as an aupair J1 visa holder.
My visa is ending on December 4th.
My aupair company which provided me my J1 visa will provide also my
flight ticket to my country for December or January.
After my program ends I want to study here in Chicago for a Bachelor Degree.
I had 2 year degree from my country Turkey. Now I am gonna
get my transcript and continue for a Bachelor degree.
My problem is I do not know if it is better:
- Register a university
Start to proceeding to change the visa to F1 here
in December go back to country to see family with the free ticket
in Turkey get approved the F1 visa and come back OR
- Register a university
in December go back to Turkey with the free ticket
in Turkey apply for an F1. OR
- Extend the aupair program J1 visa
in December go back to Turkey
come back and change the visa to F1.

I am really confused. I want to see my family before I start studying.
It is complicated. Can you suggest me?
Thanks

My visa doesn't have 2 year rule.

It will be easier for you to choose your best option once you are admitted to a university and know when you will be starting classes.