Yes you can buy your own gear to use, you can't do that modem wise with At&t

I would use the TP-Link TC7650 3.0 High speed cable modem. I use it and it works great with their service (not on their list after the 2019 update to it), it also can handle their fiber service if you ever opt to upgrade that after they stop trying to charge a 200$ fee to install it.

For the router the Asus RT-N66R Should be more than sufficient for what you listed you use it for.

It's a bit of money for up front cost, but the upgrade is really worth it. There are cheaper cable modems and routers available, but these should keep you future proof for years to come. While I still have some issues with my connection it went from occasionally, to extremely rare. I am talking maybe twice a year I will reboot my router, which I think has more to do with I bought it when it was originally released, and I have yet to purposely reboot my cable modem.