I have RetroPie on my Raspberry Pi3 B+ connected to the tv to play.it needs to be whatever OS you are running on your pi. i.e. some flavour of linux, and not windows, and obviously the games need to be able to run on very low powered hardware.
Please clarify: are you asking how to store them, where to store them, how to connect the storage, etc.?I have RetroPie on my Raspberry Pi3 B+ connected to the tv to play.