MacOS – Upgrading from Leopard to Mavericks

Yes, you can. Download and run the installer from the app store, click continue and agree to the license. In the screen asking for where to install, click the show all button to show drives other than your startup drive. You can select either an empty drive or one with older versions of OS X installed.

Since you are very likely to install OS X Mavericks again, you can make a copy of the installer to avoid having to download it again. Make a copy of the Mavericks Installer app in your Application folder before the installation begins, since the app will be deleted after the installation. You can use it to install OS X Mavericks on another drive or Mac. See here for more discussion: Re-use Mavericks install file

Reference: http://www.macworld.com/article/2055518/installing-mavericks-what-you-need-to-know.html

You could pick this route:

1. Back-up everything you need
2. Format your disk (this will format/clean Mountain Lion and all files)
3. Install a clean version of Mavericks
4. Put back the files you still need

Why this way?
Easy, you won't have the old Mountain Lion files on your file system. This results in a clean new environment to start with.
The other methods you described will result in Mavericks on top of Mountain Lion.