Well, Audie Jo, I can tell you from first hand experience that any Ducati, as awesome as they are to ride, will devour your cash in maintenance costs alone. The purchase price is one thing to swallow, but the absurd cost of parts and repairs has made me realize that Ducati motorcycles are not for anyone on a budget.
Now, as for your size, I too am 5'8" tall, though substantially heavier than you and I have no problem riding a Honda CBR 1000 RR. It can be a bit of a stretch to the pavement at a stop light due to the shortness of my legs, but you can have the suspension lowered slightly to off-set that problem. There is also the Yamaha R1 (1000cc) and the Suzuki GSX-R 1000, but not one of those bikes are suitable for a novice rider. If that is what you are, then read on.
I'm going to assume that you've been through a basic rider safety course. If not, go. Don't listen to idiots who tell you that it is pointless. It is well worth the time and cost. Also, make sure you ride with full protective gear (i.e. full-face helmet, gloves, leather jacket and pants, or ballistic nylon jacket and pants, and above ankle boots). This is a must for anyone looking to survive their first run in with a 4-wheeled idiot, or for surviving your first serious mistake. Riding with full gear gives you the best chance to walk away with minimal injuries.
Best sport bikes for beginners are in the 600cc class. Honda's CBR600 F4i is great because it has a relaxed upright riding position, delivers power smoothly to the rear wheel, has plenty of power for a beginner and won't kill you on price. They went out of production after 2006, so you'll have to buy one used, but well worth the cash.
Other notables, and in no particular order, are Honda's CBR600RR, Yamaha's R6 (600cc) and Suzuki's GSX-R 600. All can be a handful if you get cocky, but if you ride within your limits and not over your head, you'll do well with any one of those. All have excellent braking systems and all handle exceptionally well. They're all light, quick and manueverable and that's what makes them fun. And, they should fit your frame with minimal adjustments.
Good luck!