It's not often I tell people to Google, as we don't really like that on SitePoint, but in this instance it really is the best course of action:
Some of those links for you:
CentOS is a Linux distribution, it's based off of a well known distribution of Linux and is used by many hosting companies - Your best bet is to get an old PC and try it on there, or a cheap VPS from somewhere like VPS.net and have a play around with it.
Installing MySQL with CentOS is pretty trivial for the standard version that comes with the OS i.e.:
yum install mysql-server
Similar for PHP:
yum install php
Although to work with nginx you'll need to do a bit more than that as advised in the above articles.