Can I use Membership like this?

I’m looking to build a new membership site that supports an existing consulting practice. I really want to use Membership to do this (and believe I can), but I’m not sure of exactly how to do it. All I’d like to do is:

1) Have one login page that members can use to login to and be directed to the membership that they are associated with.

2) Build whatever membership are required (clearly Membership can do this part).

All of the members are manually placed into different membership levels and they don’t change over time, so that’s literally all that needs to happen. Payment takes place elsewhere. So that said, is there a shortcode or something that I can use to drop onto a page that will allow people to login and simply be directed to the proper location within the site?