Best Tyres for Grip and Puncture Protection

Apologies in advance because I imagine the tyre question gets asked a lot. I am looking for tyres that have good puncture protection (as roadside maintenance is my kryptonite), good grip (as the last two times I have been out, my bike has slid out from underneath me going around a normal roundabout at normal speed) and not costing the earth.

My tradeoff is that I do not mind (too much) about speed or weight.

I was thinking of Continental Gatorskin DuraSkin. Anyone any thoughts?