May I suggest an alternate albeit more expensive option - PSP Go
You can pick up a boxed PSP Go for around £100. It can do the following whilst being very portable
Play native PSP content
Audio player, video player, photo viewer
Play PSX games using the PSP Go built in emulator (POPS) I have yet to find one of my PSX game that doesnt work
Other emulators I have on mine. Some work better than others, some I would class as 'experimental'
Snex9xTYL - SNES
ScummVM - RPG specific emulator
PicoDrive - Megadrive
PSPUAE - Amiga
DosBox
TurboGrafx-16
Homebrew - I only have Doom-PSP 0.05 plus on mine, but it plays perfectly
It has bluetooth so can connect to bluetooth devices like speakers. I have mine hooked up to an official Sony DS3 bluetooth controller
It can be connected to a TV to output to big screen / monitor
It can sit in a seperate PSP Go cradle so it charges and connects to a TV / monitor at the same time. This then transports it into versatile PSX.
Battery life is fantastic
Screen is really good
Can connect wired headphones/earphones using 3.5mm or bluetooth. I used airpods sometimes
There are downsides;
Cost - It's way more expensive than a Pi or even laptop. In total i've spent £300 but that includes the boxed PSP Go with instructons, official carry cases, charger, hardshell clear case, 2 x 8GB M2 memory cards, Sony official component AV cable, smart mount for DS3 controller and the PSP Go cradle.
Storage - It only has an M2 slot. 8GB cards are cheap but a 16GB card expensive. An 8GB card can fit a lot of content though. It does come with 16GB built in storage so enough for most people.
Only one bluetooth controller can be connected. This means if you want 2 player games, one person has to use the PSP Go
The charger is a Sony proprietary cable
PSP native content output to tv is letterboxed quite badly. PSX content works great. Other content output to TV varies but for SNES specifically its still very good and plays games well
No method i've found yet of conntecting other wired USB controllers. Might be possible using bluetooth > USB hardware dongle of some sort
That being said, it's a wonderful device for retro on the go and emulation once it's setup right...