I would like to know what is the most lighwiegth options of running PHP on linux. I think nginx is quite CPU/memory efficient option. Is it possible to run PHP directly under nginx? Other suggestions?
Nginx or lighttpd will be the fastest free solutions. You can't get much faster than litespeed though. There are lots of tutorials available for getting a server set up with fastCGI. Give that a try.
Nginx is much faster than lighthttpd, go with that (and easier on the memory usage). I'm sure there are some tutorials on how to configure it.
Honestly, I would go with nginx but if you are a newbie its not easy to configure. However there are great tutorials out there.