Important facts:
1. Any bike, even a 250, will haul 300+ lbs without it significantly engine performance. The issue with smaller bikes and heavier people is in the suspension, not the engine. “Beginner” bikes typically come with non-adjustable suspension thats undersprung for us heavier folk. You don’t start seeing fully adjustable suspension until you start getting into bikes that no beginner has any business being on, unfortunately. An upgraded aftermarket rear shock will fix that, though.
2. The Ninja 500R has been discontinued. The 650R is its replacement. Kawasaki actually ceased production of the 500R in 2008 and all “new” models you see are actually left over from the last production run. 650Rs are respectable beginner bikes.
3. DO NOT start out on a 4 cylinder bike such as the CBR600RR or Ninja ZX-6R you mentioned above. You will make the learning process even more difficult for you. Stick with twin and single cylinder bikes due to their more manageable power delivery.
4. Since you’re dead set on sportbikes, here is a small list of beginner-friendly sportbikes out there. Note that most of these aren’t ACTUALLY sportbikes, but rather standards that are wearing sportbike bodywork.
Hyosung/UM – GT250R, GT650R
Kawasaki – Ninja 650R, Ninja 500R, Ninja 250R
Suzuki – GS500F, SV650S/SV650SF
Yamaha – FZ6R
These are the only current production model motorcycles you should be looking at as they are the only beginner-friendly bikes currently out there on the new market that a beginner has any business on. Aside from the SV650S/SV650SF, which is in every sense a “true” sportbike, all of the bikes on this list are actually standards that are simply styled like sportbikes. Honda unfortunately does not make any bikes that meet your requirements.
5. Your height may be an issue on sportbikes as their seating position forces you into a tuck which taller riders like yourself with naturally find VERY cramped.
Now, some things you should know IMO. I have been riding for two years and I still own my first bike, which is a 2000 Suzuki SV650 naked that is completely stock aside from an upgraded rear shock. When I first bought it, I weighed 335 lbs and my weight was somewhat of an issue on that bike. Even after having ridden for a year I was still struggling with many basic MSF techniques. It wasn’t until after I lost some weight and dropped down to about 275 that I was able to do things such as the box. Sportbikes simply aren’t built for big guys like us. Not smaller ones anyway. I’m going to give you a piece of advice someone once gave me as a big guy that I wish i had followed. Regardless of what type of bike you want, learn on a dual sport or supermotard-style bike. A Suzuki DR-Z400SM WILL do the job, and very well. If, after a year or so you are still dead set on a sportbike, trade in your dual sport or motard on a proper sportbike. This will allow you to bypass the beginner bikes and move into the bigger sportbikes that are more ergonomically friendly to us big guys.