Hello! Welcome to the forums. There were a few posts covering this. Obviously this one, but ignore the fact that it has a bigger screen. You could no doubt use the pin outs for the adaptor board to suit whatever display you want to use.
Here’s a compatibility criterion you can follow regarding: ordering a display.
Since this is a very similar topic to ones already started, I’ll just post this here, re: discussions on staggered pixels. As mentioned, I’m personally a fan of it. Pixel perfect renditions of older games simply doesn’t work without a lot of extra post processing, and a larger/higher resolution display.
It’s worth mentioning that there was once some talk of clockwork working on a new screen. But with the state of the world being what it was, there may have been a delay.
Besides that, if you’re wanting a quick buy it now plug in solution, the game shell is a custom bit of hardware. You’ll have to do some modification to whatever you decide to put in. Not many people have done it, since it’s a lot of trouble.
See this post for some discussions re: people looking into getting it changed over.
Hopefully this will be enough of a start to get your next project up and running.