Hi Guys.
I weigh about 200 lbs with my leathers on. I'm old and fat, actually.
the bt10s are Bridgestone radials. The important thing with the tires is not necesarilly to get a certain brand (eg bridgestone or michelin or whatever) but rather that you swap out the OEM "bias-ply" tires for "radial" tires.
Do a Google search about the difference between bias-ply and radial tires. Bias-ply are old technology. Radials are 1)stiffer 2) lighter and 3)flex more consistently.
Unfortunately, there arent many sets of radial tires made to fit the 2.5 and 3.5 inch rims on the 250, and thus we're somewhat stuck with using bias-ply tires like the bt45s or the dunlopls that come standard on the bike.
BUT..... what you can do is what I do: use a 110/70/17 radial front (easy enough to find) and then find either a 120/70/17 radial FRONT (very common size) and use it ON THE REAR. Or you can find a 130/60/17 FRONT from a hayabusa and use it ON THE REAR.
i actually prefer the 120/70 on the rear. It's s a standard front size for alot of bikes eg. 600rr, r6, r1, 1000rr etc, so it's super easy to find. I see guys here talking about going to a 140 or 150 rear, which may look good if that's what you like, bu really will degrade your handling because it's too heavy and slows down your turn-in, acceleration and braking. If you look at the fast guys on little bikes, eg. 125 2 stroke GP bikes, they run SMALL tires on the back. Your ninja 250 simply doesnt have enough power to either 1) push a big tire or 2) make a small tire break away. Small and light is always better.
Don't worry about using a front as a rear. It doesnt matter regardless of what the tire guy tells you. I raced 125s years ago and this is exactly what we had to do to fit tires.