At this point it would be best to crack open the case and get a good look at the card.
You can compair it to pics on amiga hardware sites like:
http://www.amiga-hardware.com/Infact, just looking at the pics on this site and the back of your Vid. card should tell you which one you have...
As for being a long termer/neewbe, Join the boat. I used to WORK on the beasts and now I'm lucky to navigate a CLI!
IF you DO have a Z-II version, I'd follow chiark's advice. EGS is old but is free and has some fun add-ons that I haven't seen on any other Amiga graphics software. Example, You can have your monitors side-by-side and move across them real time like you can NOW with Windows... CyberGFX and P-IV software don't do that to my knwoledge

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Good luck and keep us posted!
PS- The memory on a video card won't show up with your chip or fast ram in SYSinfo, FYI.