Support for PS1 games in PS3 is not native as in hardware, but emulated. It's ok, but it's not as good as original hardware or even the PS2 (which some are full original hardware, others partial emulated I think). One major issue is lack of 240p support on the PS3. Your PS1 games will be output at 480i (if using analogue connections) or upscaled (relatively poorly) to 480p or higher depending on your resolution on the HDMI output. I've also noticed on the 'twitchier' games, there is more issues with latency versus original hardware of course.
I've also tried patching in PS2 support on my Super-Slim PS3 but again, it's emulated and to be honest, worse than just connecting up a PS2 or getting one (they are also just about staying cheap, starting to go up). The PS2 emulator solution isn't perfect and also does some kind of dynamic resolution scaling which looked really bad on my flat panel.
I've gone with the following:
- PS1 Original hardware soft-modded with tonyhax/freepsxboot. Hoping some of the ODE solutions get cheaper as that laser isn't going to last forever.
- PS2 'Fat' with a SATA adapter and an old DVR 500GB HDD running FreeMCBoot and OPL to play my backup games. This gets used by far the most.
- PS3 Super-Slim on stock firmware (tried HeN and it was fine but didn't use any of the functions in the end so went back).
The PS1 and PS2 are connected to a 4:3 21" Trinitron CRT via RGB and are glorious. Loving going back and playing thorough some of my childhood favourites again. The PS3 was also connected to that but on balance the PS3 is better on a nice flat panel via HDMI, so it's connected to my LG OLED along with the PS4 Pro and it looks great on that. Many PS3 games are widescreen optimised and text is often not readable on a CRT.
The only thing I'd say about PS3 is that it's probably the worst generation of PS for performance (on balance, I know PS1 games are mostly 30FPS or lower). The image quality on that generation of games isn't great, lots of bloom, weird shading effects (many games are yellow/brown for some reason) and most games don't run at either the native 1080p that could be supported OR 60FPS. I find myself playing most of the big games of that generation on PC instead, and using the PS3 for titles such as Gran Turismo 5/6, Red Dead Redemption and Ridge Racer 7. I would recommend Ridge Racer 7 as it actually runs 1080p 60FPS and looks good still. One of the few on PS3. That said, there is still a huge, very cheap library to choose from so I'm sure you could find some good games.
Not sure about the state of getting hold of extra PS3 Controllers - most, like PS2, are getting quite old and there are no good new 3rd party ones I've tried. Fortunately my PS3 is one of the newest, so controller and battery still going strong, but something to also consider. Not sure if there are solutions to get PS4 ones to work or something.