I have the same thoughts (UVerse 2Wire router) - I know you can change the password on it. I would really like to use my own router behind it (because the range will be better) but have heard it is very difficult to set up.
I use a my own router \ as a wireless access point. Turn off DHCP, hook up to the AT&T router via LAN ports (instead of the WAN port on your router), and configure away.
Definitely change the default password that’s on the side of the AT&T router.