For a first bike I would look at a Versys 650.
They are a great bike and have been bike of the year. Will fit a bigger guy well. Have plenty of power and more refined than the KLR. People do put dual sport tires on them for adv riding. You can get them for a cheap used with low miles. I have had a KLR also great bike, but the versys has a better suspension, better brakes, and a better motor. The Versys is a great bike. Also had a ninja 650 a great bike, but a guy your size may be a little cramped on it.
Love the Speed Triple. It is a great wheelie bike and from KTM the Super Duke is also a blast to ride. Most of your sport bikes are great fun.........above 140 mph. On the street, unless you ride around in 1st or 2nd gear, they are a dog. Most of them do not create smile power until you are above 8,000 rpm. So unless you put a big sprocket on the back of clutch them up, they are just ok on the street. If I remember right it was about 70 mph when coming out of 1st gear on the zx-14 if you are running it hard....
I currently ride a Concours-14....think zx-14 touring bike. Not as fast as a zx-14, but very fast for a touring bike. I have been in 46 of the lower 48 states with this bike and have close to 80,000 miles on this road bike.
Even drag raced it at times.