[Water Warrior 2]

Hmm, you may be pushing the envelope a bit with a GZ. Are you familiar with the Suzuki S-40(Savage 650)?? It is a slightly larger size bike with a 650 single cylinder engine. Basically the GZ's big brother in many way. Still not a rocket by any means but likely just right as a first bike for you.
Spend some time doing test sits on various bikes to get a feel for them. There are a lot of older 500 and 600 twins out there that would work nicely too.
Primarily you want a bike that you feel comfy on. Find a few and then research them on the net. Name the bike and add FORUM after it. Works like a charm. Don't spend much time on forums that are concerned with loud pipes and chrome. But do get at least an introduction from the members and read between the lines.
My choice is Japanese bikes because they are cheaper with no real exotic designs that cost an arm and a leg to repair if something breaks. Parts are readily available too. Ebay when all else fails. Please keep us updated.