Multiple Membership Types

I’m looking to create different types of membership that people can select on logging in:

Let’s call them:

1. Teacher (free)
2. Teacher (paid)
3. Student

I would like each of these to have slightly different options in their back end. For example, I want to code a badge that people can include on their website and it will be slightly different for free or paid account, whereas a student account won’t need it at all.

I would also like to be able to put people on a different mailing list depending which type they choose.

Is this achievable with BuddyPress or anything else? Would be interested to hear if anyone has been able to implement something like this.