First off, welcome aboard! Riding never gets old and buying your first bike is an exciting experience! Just to warn you, be prepared to spend countless minutes every day thinking of riding .
So it looks like your requirements for a bike are:
-Lowish seat height
-Fair amount of power
-Mostly dirt/Some road (maybe to get to dirt?)
-Meets graduated license requirements (I don't know ozzy laws )
-FUN FUN FUN!
Manufacturer aside, I think a slightly used Suzuki DRZ-400S would be at least a good choice. I've never owned one personally, but from what I've read and discussed with owners it seems as simple as my DR650 to keep up and running. Others may say start with a 250 (Kawasaki KLX or other) but I think if you're wise enough to ask for advice you should be ok to handle something with a little more power that you could grow into. If I could spend $5k on a new bike as a new rider, I'd put $3-4k of that to the bike and the rest to gear (maybe crappy gear at first so to not waste money if it's not for you) or an adventure/trip for you and your new bike (Indonesia??? ). In general though I'd look at a lightly used bike for your first bike since you may not know exactly what you want yet. For example, I began on a Ninja 250 but I'm glad I didn't buy it new because I decided I liked dualsports more. Now I'm on a DR which I never thought I'd see myself getting when I began riding.
Remember to keep your mind sharp, ATGATT and SIPDE while riding and you'll always be ready to have fun !
EDIT: Oh and sit on the bikes (even new ones in a showroom) before going out to buy one (new or used)! That way you can get a feel of the weight under you, how much control you could have, etc.