Well first of all,

to the forums! And yeah, Enduro = Dual-Sport. As for the selling your jeep and purchasing a Dual-Sport. Do you have another vehicle for transportation? Also, have you ever ridden a bike before at all? If not, most of us around here will recommend the MSF safety course. It lets you learn on someone else's bike how to use the clutch, throttle, brakes, etc.
Also, if you want, I'm up in Northern Phoenix, at MMI (but I live at Glendale/I-17) and I'm more than willing to check out prospective bikes and help you learn how to ride. Anyway, welcome to the forums again, let me know if I can be of any service!
Wrider
EDIT: Your questions!
1. Yes, gas mileage is usually pretty good for bikes.
2. Depends on what kind of riding you're gonna do, if you're gonna do some off road, some on road, then yeah, they're great. If it's mostly gonna be onroad with some offroad you may want to consider an adventure bike.
3. 650 is a questionable beginner's bike in the dual-sport category, even for big guys like us (I'm 6'2" and 280 lbs) Personally I'd probably recommend a 450 first bike. (Keep in mind most dual-sports are very tall in the saddle to keep suspension from bottoming out).