I happen to write about driveways for a living... (among other things!)
resin bound (as opposed to resin binded) are by far the best. but are expensive.
As long as you get an excellent contractor who is experienced and attention is paid to the sub base for drainage, you shouldn't have problems with it being icy. You can expect it to last as long as 30 years - compared to around 10 years for most other driveways. Also resin is practically maintenance free.
That said, a nice brick paved driveway looks lovely and although it needs maintenance, is a nice stable driveway when laid correctly.
Asphalt and concrete will crack and crumble and they need to be sealed yearly to prevent stains and fading. But they are quick and cheap.
And you already know the drawbacks of gravel - stones disappearing into the soil and needing topping up, stones getting everywhere, needing to rake it regularly, rutting, and weeds.
Many people are going for the environmentally friendly approach of a simple soil driveway. it can look lovely but the soil needs to be topped up with Stone for stability.
there's loads of articles online about this (not just mine!)