I don't think your CL matters just if you can do the missions or not.
To join a faction you need to find a mission terminal for the faction you want to join and do missions from it. As you do the missions you will get faction points. You need at least 200 to join. Once you have your faction points, go to a recruiter and join up.
There is an Imperial mission terminal in Bestine by the shuttleport and another at the Imp base on the hill beside the town (Bestine).
There is a Rebel mission terminal in the back of the cantena in Cornet. It is behind the bar. Or you can go to any Rebel base, there should be one there somewhere.
There are recruiters standing next to the terminals, at least at the 2 I mentioned there is. There are other terminals scattered throughout the galaxy. Some player towns have them as well but no recruiters.