I'm a similar build, and took the course as well like a year back, did the EXACT same research for the same question.
General summary of what I heard/found
You will get bored of any 250cc bike quickly, but you can and will kill yourself if you get silly on a 600 or bigger sport bike (GSXR etc)
I had a 500cc Suzuki for a few months that I puttered around on, but it was a POS. After that, I decided I'm going to buy a SV650, or Honda NC700 at some point in the future. They 'sporty' bikes, but aren't crotch rocket caliber of speed, but handle very well, hold value well, are more beginner friendly, etc, etc, etc.
If you are looking to buy a beater first bike, then just buy a older 250 (Ninja *Sport* or Shadow *cruiser* for example) until you are comfortable riding on the road, and then get something 'bigger'.