This link should help you get an idea of what you are doing on the installation.
You don't have an option for "install to existing partition" because it did not find any linux format type partitions, since you have not created any as of yet.
If I understand right you have a thirty gig drive that is one partition, and about 22gigs of it is empty but formatted as ntfs. So you are going to use windows. More specifically you are going to resize your windows partition to a smaller size, leaving empty unpartitioned space to create your linux partitions. Once you have free space you can auto allocate the space using Mandrake install cd.
Partition Magic can be used for shrinking your current ntfs partition to make room for linux, as well as Qtparted on a linux live cd such as Knoppix. Can't remember if Mandriva's partitioning utility can resize an ntfs partition or not as I have not had windows on my own pc's for a while now. Ok, just checked and Mandrake since version 9.1 has been able to resize ntfs nondestructivly. That is your option #2 that you said you don't want to use.
I suggest back up anything you really would not want to lose, and go for it. (I have never lost data due to repartitioning or using linux, although I learned the hard way due to hard drive failure)