When building or rebuilding a server what LAMP (linux, apache, mysql, php) package do you use? Or do you install each application individually?

By default, Cent OS has its own running apache, however this would be easy to be installed if you use cPanel. Through cPanel's easy apache functionality, you will be able to install or update PHP & Apache.

These softwares are installed automatically, with regards to mySQL cPanel has its own mechanism to update that module.

Most of the time our servers run cPanel, when running client or public services.
Dev servers and management servers normally run a CentOS basic minimal install, with a basic Apache, PHP, mySQL package downloaded from yum repo's.

Well I use to use Gentoo OS and then install php, mysql ,phpmyadmin and then install cpanel but that use to take so long so I tend to use Ubuntu now with php,mysql and cpanel installed