Download PSN PS1 games from Sony servers (registration required)
Official Eboots have superior compatibility, but their number is low.
Convert ISOs to Eboots
Convert your own PS1 ISOs into Eboots using PSX2PSP.
If you are having some trouble with converted eboots, be sure to download Popsloader v4g here. Most of the games will work without it nowadays, but for those that don't, you'll need this. See popsloader compatibility list(slightly outdated).