Custom and browser agent logging

I wanted to log browser agent, screen size, timezone (including current system time). This is my first go at any web server (wordpress is my first install). I wanted to do this without plugins by editing the httpd configuration file.

Can someone please guide me? Also I was reading apache documentation and there was a warning for write access to logging directory reducing security. What is the best way to have logging and not reduce security of the server?

cheers in advance!