Hi Latinga, and welcome to the discussions.
With any luck, your problem is simply that your new hard drive has not been initialized, which is why the installer can't find anyplace to put the OS. It's a simple fix:
1. Boot from the first Install disk.
2. At the first window (in 10.3 is the Language window), go to the Install menu at the top of the screen, and select "Launch Disk Utility". Disk Utility should show your new hard drive in the left-hand column as an icon with the manufacturer's name followed by a series of letters and numbers (depends on the manufacturer and size, ie. Toshiba MK3018GAS). Select this icon.
3. On the right-hand side, choose Erase. Your Volume Format should be Mac OS Extended. Give the volume a meaningful name, hit the return key, then click on Erase. In a few seconds, the left-hand column will show the icon with the manufacturer's name, and, below that and indented, another icon with the name you just gave it.
4. Quit Disk Utility. You'll return to the Installer program and the language window. Continue the installation, and when it reaches the point where you choose your directory, your volume should be listed.
Let us know how this goes. If you have any further questions, don't hesitate to post back.
Andrew