With TinyXP Beast, I think you still need to have an empty partition first. On my PIII, I experimented with TinyXP and DrewKaree's Nlite setup. I didn't want to destroy my data, so I used PartitionMagic to create some new partitions and then did the install using the TinyXP disk.
One problem I did run into was that my old Dell PIII has an ATA Ultra PCI card that the drives connect to instead of the motheboard IDE connector. You need to have the driver for this card at install time in order to install XP correctly. Otherwise, at least in my case, the install wouldn't complete. The normal WindowsXP disk will contain the necessary drivers, but the TinyXP and NLite installers don't. In order to do the install, you'll need to have any required drivers on floppies.
Once I figured out it was the Ultra card that was giving me problems (and it took me a long time to figure that out), the installation went smoothly.
In the end, I opted not to use a TinyXP installation and just kept my old one. The TinyXP install did boot faster and take up less disk space, but it wasn't running games any faster than my normal XP install. Instead, I just used Windows to disable a bunch of the services that I didn't need, and uninstalled a bunch of junk that was launchng at startup