Ok I wanna chime in here. My vote would be for the Yokohama AD08R. Yes they are expensive but they offer excellent grip in either situation.
I have had these tyres on my R32 GTR for the last 2 years and have done countless weekend and weekday runs whether it hot or pissing with rain, also done 3 track days on them. Never had any issues with the car feeling unsafe in the wet and the car puts down 460kw at the wheels on 17psi of boost so its no slouch. Can i get it to light up all fours in the wet, of course but you drive to the conditions. I will agree that when its warm and the road surface is kinda gravely they will throw up stones, so either get you're lower guards clear wrapped or accept it.
The tyres I had before these and have them on once again (because i got them cheap ) are hankook Z221 semi slicks. They are more track focused, definitely provide more grip at the track but are quite a bit louder to drive on the street. Once again the car still feels safe in the pouring rain on the road, just don't be an idiot and you will be fine.
My lap times were still pretty decent with the AD08R's, just make sure you check pressures and keep them at suggested hot pressures and they provide plenty of grip and confidence. Definitely the pick of the crop if you want a street and track tyre.
I will be trialing a set of the newish nankang semi slicks on a different car in December at the track and will give some feedback then. These things are dirt cheap and people that i know that have tried them have said for the money they are great.