Although the Honda CBR300R comes with bias-ply / cross-ply tires as original equipment there are several very good, higher-performing radial alternatives these days and what might surprise you is that some of them are cheaper than the bias-ply tires.
In the 110/70 R17 and 140/70 R17 sizes Bridgestone make their S20 EVO, which is very good in wet conditions. Continental make their very high-performance Attack SM, Michelin make their Pilot Street Radial, which is different to their standard Pilot Street, and Pirelli have their Diablo Rosso II.
Mitas also has excellent tires whichj are not expensive. For example the Mitas Sport Force+ 110/70ZR17 and Mitas Sport Force+ 150/60ZR17 .
Because it looks much better you can upgrade your rear tire from a 140/70 to a 150/60 or even a 160/60. I think the 150/60 is a good choice between looks and handling.
I have a Honda CBR300R and I’m considering changing the IRC tires as they are useless in the wet and the front doesn’t inspire any confidence. In some corners I feel like the front is going away from me and have to lift the motorcycle up. What should I fit?