To upgrade... Boot the installer DVD (on 10.6.8) and make an external backup. Or two. Upgrades don't fail often, but they do fail.
Then purchase and download and install Mountain Lion if you're abandoning OS X Server, or purchase and install Mountain Lion and then purchase and install Mountain Lion Server if you're going to upgrade to 10.8 server.
OS X 10.8 has the old server stuff packaged as a Mac App Store application.
Server configurations are preserved, though some server capabilities (such as Podcast Producer) are removed.
Server.app management is quite different from the classic OS X 10.6.8 Server Admin.app and related. Apple has simplified things considerably. (For good and for bad, depending on exactly what you're up to.)
If you don't want the old contents and detritus on the disk preserved, perform a nuke-and-pave clean installation of Mountain Lion.
If you're going to be running OS X Server (any version), make absolutely certain the local DNS services configuration is correct, or weird problems ensue.
The Mountain Lion specs have details on the contents, and links to the Mountain Lion Server details.
FWIW, "nervous" is seldom a reason to do anything, though it's certainly good fodder for folks looking to sell you something. Best to figure out why you're nervous and whether there are specific concerns. Then figure out what you're doing about those concerns, and why, then evaluate whether an upgrade makes sense or not. Nervousness can be part of the foundation of FUD (Fear, Uncertainty and Doubt) marketing, which is an effective way to sell stuff.