The phone is pretty old, running Android 6. It has 2600.emu on it with the entire catalogue of 2600 games. She remembers playing on her friends' Atari as a kid and some of the games she played so I added those as shortcuts.
I tried several emulation apps: 2600.emu, droid2600, and MAME4Droid. The modern versions of all refused to install. 2600.emu and droid2600 both had an older version that installed. Overall I liked 2600.emu for its better onscreen controls & better paddle control on these specific versions.
It feels nice to repurpose old tech for something "new". It wouldn't be possible without a dedicated community.
The controller is almost certainly an HID compatible controller that will work with any application that supports controllers.
As for a stand, I recommend a pop socket-style thing, as it permenantly attaches to the phone.