I know that a lot of third-party PS4 wired controllers will work right out of the box for the PS3.

A lot of things on the PS3 store are silently vanishing off the online store. There's still some games, but the library is getting smaller all the time. There were a lot of PS2 and PS1 games still available the last time I looked, but who knows how long they'll be there. You might just be better off buying a PS2 and PS3 (or a PS3 with backwards compatibility, but those have a higher failure rate). PS3 game prices have gone up in the past couple years, but it's fairly easy to get games for it since people are dumping their old games in retro game stores right now. I'm not sure about PS2 game prices.