I also have the car all season Generals on my modded SI. performance is great in the rain and dry. I live in the south, not really a worry about snow. Currently I have the West Lake tires on my F-Pace. They came with the car. They are cheapest you can find apparently. I think they do well. I've been through heavy flooding on the highway and recently through heavy mud to a camping site. I may actually get them again.
Also, if you get a lower profile tire, then you will need bigger wheels to offset the change. Calculator for ya.