membership software for an association

Could you recommend software that an association can use for members to create accounts and submit membership information (name, email, phone, membership type [student, full-member, etc])? The association already has a domain name, web host, and website. The members would submit membership info via the website.

Could the software facilitate electronic payments, or allow the association to update members' payment information after the member mails a cheque to the association? The software would help the association keep track of membership status, payment of fees, date joined, date lapsed, membership type, etc.

Can the association email categories of members? For example, an email just to current members. Or email only to members who forgot to renew the membership this year. Or an email just to the student members. Would this be easier if the software saves the member info as .ods?

The association is open to commercial and gratuit options.