It seems like only the music I purchased in the iTunes store is transferring and I'd like to get the music I've ripped from my CDs onto my new MacBook but there is no CD drive.
You are looking for iTunes Match. It's a $24.99 a year add-on that will allow you to d/l from iTunes anything you ripped to your iTunes library. I don't think it works tho from just music already on the phone, it has to be ripped to your library using iTunes.
You can use the free application iFunBox for Mac or Window (http://www.i-funbox.com/) to access the files on your iPhone from your new computer and simply copy the music files to your new computer.