Hello Hugh,
Always start by increasing the front sprocket size if possible. Larger sprockets mean less angular acceleration and thus a longer, happier life for the chain. Smaller sprockets may require shortening the chain and may also cause increased wear on the swingarm pads. Stock Honda CBR300R's come with a 14-tooth front and 36-tooth rear sprocket, giving a 2.57:1 ratio. Go up one tooth in front and you will get a 2:40 ratio, giving you a 7-percent reduction in engine rpm at a given speed, and you can use the stock chain without alteration.
Try this before reducing the rear sprocket size. Aftermarket 15-tooth front sprockets are available, affordable, and relative simple to fit.
I'm interested in the Honda CBR300R and, if I buy one, would probably want to change the final gearing by replacing the rear sprocket with a somewhat smaller one. Having ridden (and learned from) an Italian 250cc single in the '60s, I'd be glad to exchange some acceleration for a more relaxed and smoother ride at higher speeds. Are there any rule-of-thumb suggestions for such a swap?
Hugh