PS1 emulator console is, as you expect, a console that uses a PS1 emulator and peripherals to work similarly to the original PS1 console. The emulator I use is called PCSX reARMed due to its ability to run on a arm processor. Games for this emulator will be taken from any PS1 game CD via an attached CD drive. Finally, the game controls will be inserted from a PS3 controller via Bluetooth connection.
The instructions on set up and operation of the console is mentioned in the linked GitHub repository.
Here is a video of the console being used:
1) Look into possible ways of running games from the CD so download time can be reduced or eliminated
2) Improve output audio so the random audio cuts stop
3) Implement project for a Raspberry Pi to reduce total cost by at least $20