I have a brand new macmini. It comes with mavericks and I haven't booted the machine yet. I know for certain that I will erase mavericks and install 10.6. However, if things go wrong, I would like to be able to reinstall mavericks. and restore the situation as it was as out of the shop. What do I have to do in order to achieve this ?
No you won't be able to install Snow Leopard, it's not compatible.
But you'll be able to build app that a compatible with older OS X from XCode. But you won't be able to test it's behaviour on older platform from this mac. You'll need older macs.
Chances are 10.6 won't work on your Mac Mini. As this hardware didn't exist when 10.6 was the main OS X version it probably doesn't have the right drivers for your hardware.