Don’t get a bigger displacement bike. Their bottom-line of 650cc should be at the very top of the range you consider. As a fellow sportbike rider, you need to take your peers’ advice with a whole shaker’s worth of salt. Even among expert racers, advice varies widely from useful to macho bullshit. (It’s not uncommon for racers to tell me that I just need to “whack open the throttle” coming out of each corner. Even professional racing instructors will tell you that this approach is idiotic.) The most important thing to consider as a beginner is power-to-weight ratio, as well as total weight. You want a smaller power-to-weight ratio, but you also don’t want a heavy bike when you’re just starting. The low-weight requirement rules out a lot of the big cruisers and tourers as good beginner bikes.
Weight is not an issue. Unless you are a small planet (and I really do mean that), just about any motorcycle will carry you without any problem. If you are on the high end of that weight range (which you’re nowhere near), you begin to run into suspension issues, and some smaller bikes will start to struggle, but that’s not an issue for you.
Height may well be an issue for you, though at 6 ft, you might not have the same problems I do at 6’4″. The real issue is your inseam, as your height might not be as much in your legs as you think. If you do have trouble sitting on the usual 250 cruisers (Virago/V-star, Rebel, etc.), I’m sure our fellow member Munch would recommend the now defunct Kawi Vulcan 500. It’s a great starter bike, especially for a bigger guy like you.