Hey,
It really seems that there is a need to combine several apps together.
Regarding signing up a member for a specific plan, you might want to check out the Wix Pricing Plans app.
As for the rest, it seems that there is a need to write back-and code to associate a certain badge or program with a certain type of user (for example if he purchased a certain package).
This is the API:
https://www.wix.com/velo/reference/wix-members-backend/badges/introduction
Any way, I think it’s best to ask it in the Velo community