Well, it's wierd that you can't find anything that works. ePSXe does great for most PSX games, as well as pSX (depending on your games) and many others - PSXeven, PCSX, etc. For PS2 you can
try PCSX2...
As for the needed files, you have to have PSX and PS2 BIOS files (you're supposed to dump these files from your own PSX and PS2. Do not ask for it here or hushypushy will come as fast as you'll never see again and close this thread, once it's against the forum's rules). If you choose to use a plugin-based emulator, you'll also need plugins (that can be found
here).
Finally, you can find the emulators mentioned - as well as many others -
here, just as JkKdArK said.