RG350P, end of story.
I mainly use it for gba, tg16 hu and CD, and PSX. I play two of my favorite games on it almost every day: Advance Wars and L.S.D.
Ended up taking this advice, except I got the RG351P instead. I was flip flopping between the two since the 351 is quite a bit more powerful, but has an odd resolution and screen aspect ratio compared to the 350.
This thing is amazing. Good build quality, the controls are great, it's lightweight and comfortable, and it runs things way better than my Pi handhelds. I just got it for like Gameboy, Genesis, maybe GBA if I'm lucky. This motherfucker plays Street Fighter 3 with no issues.
The resolution thing is a non issue it seems. It looks goofy on most systems at first, but turning on RGA scaling makes most everything look good. For the low res handhelds it's strong enough to run shaders without a noticeable performance hit.
The only issue really is that it seems to be marketed as a device that plays Dreamcast, n64, DS, and other difficult systems. They'll run, but you really shouldn't. PS1 is really the max you'd want to play on it.