Assuming he has the CDs and has a way to rip the BIOS [Which is legal, per the BLEEM case], emulation of the PS1/PS2 is perfectly legal since there's no copy protection to break on the disks, and thus doesn't violate the DMCA.
Now that I've covered my own behind, for the PS1, ePSXe and PCSX Reloaded are the best options, though other options, such as pSX, are also viable in a pinch. I'd say *most* stuff is expected to work, though a few games are finicky with savestates.
For the PS2, PCSX2 is the only option. Most stuff works these days; I'd guess about 80% of the PS2 library works, though slowdown and the occasional graphical hiccup are common. Depends on the game really.