Some users need the latest Apache and MySQL, some are happy with the well known and stable Apache 1.3 and MySQL 4.0. I would recommend using the software that is provided in your Linux distribution or control panel (if you chose cPanel or Plesk). This allows you to easily keep track of programs installed on the server and upgrade them if it is necessary.
The reason to upgrade the databases and web server is to use features that are not included in the installed versions. But keep in mind that if you choose this route, you would have to manually do upgrades in the future.
Lunarpages charges $75 per hour for script installs or upgrades. If you added the managed addon, you have one script install for free per billing year.
I will be happy to provide further suggestions if you answer the following questions. First, what version of Linux is your server running? Are you using a control panel?