That's honestly an awesome idea! Analogue and RetroUSB are doing very well with highly accurate HD clones right now, and a decent collection of PS1 games can be built on a budget if you aren't pick about what color the label is:
https://www.youtube.com/watch?v=_A8ammwz9LM
Retro Tech Select - My Youtube channel. Covers throwback consumer electronics with a focus on "vid'ya games."
Latest Video: Top 12: Best Games on the N64 - Special Features, Episode 7