Is this for a track bike or a street bike?
If it's for a street bike, the BT003RS are a complete waste - way more performance than you're ever going to use, and terrible wear life. As they wear, the handling will tend to get a little weird, because most street riders can't wear out a tire evenly. Instead I'd point you towards one of the many sport touring tires available, or at a minimum a more conventional street tire like the Q2.
For the track, BT003RS are far from the stickiest tires available in those sizes. Bridgestone's own BT003 Race tires are stickier, and there are lots of good options to fit the 4.5 inch rear you installed. If you wanted to install a 3.5 inch front tire as well, you could easily enough run 250cc 2 stroke slicks, which are available in everything from a medium compound to an ultra-soft.
For those rims, either a 150 or 160 rear is fine - just make sure that the tire will clear the chain, swingarm, and brake linkage.