The monthly rental would give you free replacement if the modem were to fail again as well as help with troubleshooting (if that ever becomes necessary) since the Sonic support person would be familiar with your specific modem model.
On the other hand, setting up a DSL modem for dynamic IP service is usually not difficult. Sonic does have setup guides for a number of different DSL modems on their support website. From the look of it, these guides seem to be for users who still have modems from a prior ISP before switching to Sonic. This means some of the steps to follow may not be necessary for retail configurations of DSL modems (no need to undo a prior PPPoE configuration).
The TP-Link TD-8816 is not on the list of modems for which Sonic Support has a configuration guide published. This could mean that you depend on help from TP-Link support or from other Sonic users who also have that modem if you need help with the configuration.
If you do buy your own modem it makes sense to select a model that a lot of people are using so that you can get help in either the ISP or the Hardware/Equipment forums.--
Got some spare cpu cycles ? Join Team Helix or Team Starfire!