Most of the early game missions are triggered by phone calls from Simeon, Lamar, and one of Lamar's friends. These should start up at about level 4. As you level more options in free mode will appear.

I personally had problems with these events triggering automatically on day 1. Day 2 seemed to be better in that regard. Though be weary, there still seems to be issues with the servers not remembering everything you've accomplished.

There are two ways to see the whole Hierarchy of your crew via the Rockstar social club, View your hierarchy and Manage your hierarchy.

To view the hierarchy of your crew:

1) Login to the Rockstar Social Club here

2) Click on the Crews link

3) Click on the crew's title that you want to view the hierarchy of (you can be in multiple crews, but only one can be active at a time). The text will turn a different color when you mouse over it. Note: I have painted over our crew as I am not looking to advertise in this answer (PM me if you would like to join).

4) Click on Hierarchy

5) View your awesome hierarchy!

To manage your crew:

1) After clicking the crews link (#1 already shown above), click on Manage Crew. Either link shown in the picture will work.

2) Click on the Hierarchy tab, and manage your crew!

If you are interested in the actual rank titles your Crew leader specifies, you can view that under manage (if you have the previlage to do so) and at the bottom of the page. Ours looks like this: