Adding router for guest wi-fi

I've searched and found all sorts of posts about bridge modes and pass-through, but I have done something simple and I want to make sure it is ok. I have U-Verse's NVG589 router for our network and private wi-fi. I want to have guest access to the Internet, so I attached my Netgear N600 router to the 589 (Netgear's Internet port to 589's LAN port). The NVG589 is using 192.168.1.xxx and the Netgear is using 10.0.0.x for the guest wi-fi. Everything is working fine. The wi-fi's are separate, with different passwords. Internet access works great on both. My question: Does this setup seem right? Will it protect my NVG589 network computers from being seen or accessed from the Guest network? Is is safe enough to even disable the password on the Guest network? Thanks.