Hi,
Congrats for your new Mac.
First it would be good to try to figure out which exact iMac G4 flat panel that is.
The serial number and the specs should be inside the optical drive cover (the flop under the Apple logo in the front). See if you can carefully lift the optical drive cover and see the serial and the specs. The spaces are what matters in defining what we can install there, as in what is the latest OS that it will like.
The other determining factors are the amount of RAM (if it's not maxxed out for RAM, that would be good to do to make sure it runs fast), and the size of the hard drive, and what type of optical drive it has (whether it reads DVDS).
This is one of the alternatives for which generation Mac it could be
http://www.apple-history.com/?page=gallery&model=imac_flat&sort=date&performa=off&order=ASC
But it may be newer as well, on the right side you see a lot of links so it'll have to be one of the models between 2002 and 2004 iMacs.
The newest system for the iMac would most likely be Mac OS 10.4.
Did they include any discs with that Mac? If the seller didn't include the discs that came with the computer (it would have had an OS less than 10.4), you'll have to purchase the install discs. (ebay etc) - but let's try to get some more details on that machine before getting into details how to install or where we can get the discs if none are present.
The first computer I've actually bought myself, too. How do I install the OS on it?