Thats great! I absolutely love my bike- just started riding last year. I started with a sport touring bike, a suzuki katana 600 (it was quite heavy, but a good starter bike as it isn't as touchy, and is more forgiving than alot of the faster sport bikes). I would also make sure you check with your insurance company about insuring your bike. If you are under 25 some companies won't touch you! Or, they may have really high rates, you can get a less powerful, or a sport touring that have much lower insurance rates.
I moved on to a Yamaha R6, that had been modified. It was a much better fit and weighed about 150lbs less than my first bike. I would make sure that you are comfortable on the bike, and that both feet touch the ground (I am only 5'6" so they adjusted the rear shock so that the bike was lower- you are tall so shouldn't have that problem!). If you can, make sure the bike you buy is certified, or has had a safety. This can save you alot of money down the road, the bike may need new tires, or any number of things. Make sure you look at the condition of the bike- the tires are important- they are expensive to replace, so make sure there is tread and they aren't at the wear bars. Do you have any friends that ride bikes? I just took a guy friend with me, and he looked at the chain, made sure it had no marks from being dropped, and checked things I wouldn't have thought to.
I have heard that the CBR 600's are a great beginner bike. Very reliable. I wouldn't suggest getting a 125 or a 250 or anything- you will grow out of it quickly and just have to replace it. On Road/Off Road bikes, like an enduro also don't really compare to a street bike either- so I would just jump in and get a 500 or a 600.
Also, just a safety spiel- make sure you get a good helmet that fits! Get it fitted at the store, it may seem tight but you don't want it falling off! Also get some good leathers, there is a possibility you will drop your bike and you don't want to get any more hurt than you have to!
Anyways good luck & safe riding! If you have any questions feel free to email me!