You can call Apple support, and they may, or may no longer have, the original disks for your mini. If they have them, I believe they were running around $65.
If not, you have several choices .... if your mini will support 10.5 Leopard (see http://support.apple.com/kb/HT3759), the online Apple store may still have it for sale, but you have to call them at 800-MY-APPLE.
Second, you can buy Tiger new from some vendors, one of which is http://hardcoremac.stores.yahoo.net/ . Don't buy an upgrade version (since you have nothing on your hard drive to upgrade from).
Third, you can buy a used copy of Tiger from ebay/craigslist/etc. If you buy used, either buy a retail copy with black faced disc's or if gray-faced, ensure it is for your model of mac mini, because the gray-faced discs are locked to the system type they are delivered with. If buying used, safer to buy a used retail (black face) version.