Welcome to the site!
Not too sure bout the Sth East burbs, but Stay Upright is where I did my licensing. If you've never ridden a bike before, I'd suggest the 2 day course in which they'll go through nearly all the basics to keeping yourself safe.
http://www.stayupright.com.au/I had a ZX2 as my first bike. As with anything, if it's been looked after (Unfortunately most of the grey imports haven't) it'll be fine. I'd suggest a new 250 ninja, or the old ZZR's/GPX's. All are great bikes and will do a fine job until you're comfortable and ready for an upgrade once you're off your restrictions.
My only advice riding is try to limit the amount of risk whilst riding. Things like not sitting in people's blind spots and positioning within your lane, if done right, can all help limit the risk. Practice is the key!
Hope to see you out there soon!