I'm with the other good folks here that say a KLR650 would likely be a good choice for you. The people that have recommended a 200 or 250, apparently missed the part of your post that says " I am 6'2'' and for round numbers 280 to 300lbs". I'm in the 5'10" and 180 range, and for me, a 200 on the street would be just ridiculous. Granted, I've been riding for 25+ years, but if you're going to be spending any amount of highway time on a bike, I wouldn't recommend anything less than a 600cc bike. Don't get me wrong here, I'm not saying that you should go out and get the biggest bike that you can find, but I will say that a 200cc bike is small in size, small in power, small in the brakes dept., and built for a person who is generally smaller in size than you are.
Find a bike that is built for a rider of your size, and for the riding styles/activities that you are wanting to participate in. Also, keep in mind that different engine designs provide different amounts of power- ie, a KLR650 has about the same horsepower as a Honda CBR250R. Granted the torque of the KLR is three times that of the 250R, but the point is to keep in mind that making a comparison based solely on cc's is not a reliable measurement of power. Most days, I ride a Buell XB12S-TT, a 1203cc bike. One of the guys that I ride with regularly rides a Yamaha R1, a 998cc bike. Comparing the two, even though I have over 200cc's on him, my bike's like an arrow, and his is like a guided missile. Apples and oranges, different bike built for different operations.
I'll also agree with the folks that say that you should take a riders safety course. Check out the
Alberta Safety Council website- there's information there on motorcycle training in your province. At the very least, you'd be wise to consider the "gearing up" course. You'll get what you put into these training classes, and if you're open minded and there to learn, the amount of skill and knowledge that you'll gain in one weekend can be equivalent to several years of learning on your own.