To get a compatible modem that you know will work with centurylink internet service it's best to just purchase a centurylink modem from centurylink but here's a few compatible modems that will work with centurylink.
Actiontec 300 Mbps Wireless-N ADSL Modem Router (GT784WN)
NETGEAR Nighthawk AC1900 VDSL/ADSL Modem Router Certified with CenturyLink - Non-bonded, DSL Internet Only (D7000) .
Zyxel C1100Z 802.11n VDSL2 Wireless Gateway CenturyLink.