Want to do clean install of Mavericks - do I need older OS on computer?
You can install from scratch.

To do so:


Download the update from the App store.
Create an install DVD or an install USB flash drive.
Boot from the install drive (Holding alt or option during boot).
Using disk utility format the desired partition.
Launch the install process on the newly formatted partition.


Enjoy the fresh install. 



Edit: One thing to note is the fact that you don't have to format the entire hard drive. You can only format the partition containing your OS and do the install on that partition.

If you want to install Mavericks on a different partition to allow multi boot (Mavericks/Mountain Lion) you can use another partition to do so as long as there is enough free space on it.

One important tip to remember is the ability of disk utility at creating additional partitions :


Open DiskUtility.app
Select the desired hard drive
Go to the Partitions tab
Under the partitions list click on the add button to create a new partition.