The numbers are the engine size. Here's my guide to the ones you're asking about, when it comes to sport bikes.
600: About 100 hp in a 400 lb package. It's possible for a beginner to ride one, but not very easy.
700: Even crazier than a 600.
1000: One liter here, and ungodly fast. Very few riders can actually push one to its limits. Even fairly experienced motorcycle journalists will admit to being scared of these monsters.
For just learning to ride, I'd stay under 50 hp. This would mean a 500 cc or under with the bikes available today (the old Yamaha Seca is an exception, a beginner friendly 600). A sport bike like this will still be pretty fast compared to most things on four wheels, but it's a lot more predictable and forgiving than a 600.
There's four choices out there that I recommend from reputable manufacturers: The Kawasaki Ninja 250 and 500, the Suzuki GS500F, and the Buell Blast. I ride a GS500F myself, but I recommend checking out all four and seeing which one you like best.
These bikes are pretty fun to ride, and if you spend your first couple years learning to ride on them you'll probably learn a good bit more than someone who's started on a 600 and struggles to keep it under control.
Also, I recommend taking the MSF (Motorcycle Safety Foundation) class or its equivalent. It'll be a big help learning to ride, and in most states passing it will get you your license. Money well spent (unless it's free, which it is in some states).