Also looking for what to avoid.
Mine is 9 years old. Just waiting for it to kick the bucket.
Netgear DGND3700 ADSL2+ modem with 2.4 and 5 GHz 802.11n Wi-Fi GigaBit Router
Verizon provided the first one when I signed up for service and when it died they provided another one free. No problems. Plug it in and go.
I’d start with AT&T DSL’s support web site and see if there are any they specifically recommend - I’m guessing they’ll support you with setting up stuff they recommend... :)
Linksys and D-Link both make good modems, routers, etc. You shouldn’t have to look much further than those two. I’ve had a D-link wireless router set up for many years and it hasn’t given me any trouble.
I had for around 10 years a Linksys wrt54g. The wireless signal went down to about 20ft range from 150ft. My bro inlaw had the same one and I bought it from him and now I am back to full range. I would buy the same one. They still sell them.
http://www.amazon.com/Cisco-WRT54G-Cisco-Linksys-Wireless-G-Router/dp/B00007KDVI
DON’T get the AT&T 2-WIRE modem. I had one for two years and the DSL kept going down. After 4 ATT technicians, I finally changed to a Motorola modem and haven’t had a problem since.
It is an excellent router, as you can determine yourself from the 3,516 user reviews.
Plus, it is designed to have the firmware replaced with open source DD-WRT firmware, which upgrades it to a commercial-grade router.
You really can't go wrong with this router, even if you don't flash the firmware.
MARK
Before you give up on your old modem, try spraying the on-off switch with contact cleaner and clicking it maybe fifty times (with the modem unplugged). Can’t hurt, may help: a whole bunch of problems I had with a ‘bad’ HDD went away when I cleaned the power switch of the mobile rack it was mounted in.