It's a G4 Mini, so no Snow Leopard; Leopard's the highest that it can go. I believe Tiger was actually the OS that shipped with even the earliest Minis, not Panther.
FWIW Snow Leopard doesn't really make much difference between itself and Leopard for nostalgic Mac OS X-ing. Most of the indie developers were swept away by the iPad before they could think to make any Snow Leopard exclusive software. Leopard also retains a number of good things for interop with classic Mac OS which were blown away by Snow Leopard anyway.
My preference is for Leopard, since Mac OS 9 on bare metal (which
is possible on a Mini through a special build) is the only one that can do MIDI. Classic mode is a gimmick that won't help with most of the cool Mac OS 9 stuff. Leopard performs well on a G4 with a Radeon 9200, which the G4 Mini has, so it checks all boxes. I think the PPC community at large has switched to prefer Leopard over Tiger over the years between more features, more software running on it, and Time Machine is just nice to have for backups you don't need to think about. That's my piece, anyway.
The flashing folder icon might indicate that your Mac just needs to be "blessed" to run Mac OS X. You'll probably need a Mac OS X DVD to get the right tools for that, since your Mac is too old to have a Recovery partition, but most of the steps outlined in
Apple's Support site are still largely relevant for getting a Mac blessed for OS X.
Can't help you out with sourcing used hard drives. The Mac Mini
needs a putty knife to open to swap out the HDD, it can be done, but you have to be careful not to break the tiny bluetooth or Wi-Fi antenna cables. Upside is you can and probably eventually want to put an SSD or a faster HDD. Aside from the putty knife weirdness and those two cables it's not the worst.