Membership plan assigining to approiate profile type

This is a Membership Plugin/Buddy Press Profile type issue:

I am building a membership site. There are three memberships plans (parent, care provider, and business) Each membership has a different price.

I have also made three profile types and each have different profile fields.

I need the user to sign up for the site using MEMBERSHIP then have them directed to the correct profile type for their account.

So if they sign up for the parent membership plan they can only make a parent profile.

Since each membership type is a different price, I cannot have someone signing up for a cheap membership and creating a profile for a more expensive account type.