Evaluating WP for membership site

I am working with a client who wants a membership site. She manages 4 different groups and wants group members only to have access to their particular group.
The plan is to have a set of links on the home page – one for each group. When the user clicks the link, he/she is shown a page with a login box. When login is complete, the user is taken to his/her group page with group-specific announcements, calendars, etc.
I am a WordPress newbie, but not new to website development. I would like to use WordPress as a content management solution for this client, but need to make sure I can implement a membership model (as described above) before I have her purchase WordPress hosting.
Thanks in advance for your help and advice.