I'm also in the process of making a PSP.
If I understand it right can the PS1 only output 320x240 so a screen with higher resolution than that would not be needed. There is screens with that resolution on eBay that are 4, 4,3" and only costs round 20-25 USD.
Like this one
If you want to make something a bit different/cooler, hunt down one of the later original playstations. The board is actually smaller than a PS0ne, though longer and less wide. Fits perfectly in a gamegear