The Rebel is a great beginners bike, but at 5'10" you might be a bit cramped on it. But that can be fixed. Ninja 250 is another good bike. We own both (well, two Rebels and a Ninjette).
Even though both are only 250cc, the Ninja is far faster than the Rebel. Geared different, I believe, and it will leave the Rebel in the dust. But I'm pretty happy with my little Rebel. Bought it slightly used in 2005 and it has just over 23K on it now. Took it to WI this past summer (5,000 mile RT). I started on the Rebel, then when I was comfy on that, got a Honda Shadow 750. My tastes have changed, and I seldom ride the Shadow anymore, but it is a very forgiving bike and its the most comfortable bike we own (the Mustang saddle helped with that......) The Rebel is my daily commute bike. I've done some upgrades to it, and at 85 mpg and practically maintenance free, it has paid for itself many times over.
A small dual sport is also a good choice, but depending on where you live and where the dirt is, well, getting there can be a challenge. Our Honda CRF230L is street legal but taking it out on the highway is ummm...well, we just don't do it unless we have to. And the newer ones tend to cost a bit more (Rebel was 3K, CRF was close to 5K) I really love my F650GS, but the only way you're gonna get one of those for $3000 is if its in pieces and a couple of them are missing. (Hmm... try an earlier belt drive version called the F650CS.)
Start small, get comfy with your skills, then move up. Lots of bikes out there. Sit on all the ones you can. See if someone will let you take one for a test ride. Ask lots of questions. Insurance costs? Maintenance costs? Regular or Premium?
I cannot say enough about the gear. I realize it is a personal choice, but for me, the $1500 I have spent on my gear is cheap compared to skin grafts and brain damage. And BTW, don't expect them sexy looking chaps to save your ass should you find yourself sliding down the asphalt.