Icy conditions will require more rigid skis that cut into the snow and don't track in established ruts.
Soft powder will require fat skis that float and flex through the soft snow.
Beginner skiers will want a ski that turns easily and doesn't go fast.
Advanced skiers tailor the skis to their particular desires and my eventually collect a quiver, each with it's specific condition & use.
Most resorts carry a nice variety of skis to rent. It's reasonable for intermediate skiers to rent a variety of skis in order to play with the style they like for the conditions of the day.
To briefly look at your metrics:
- Front tip width: Float of the front of the ski
- Middle width: Float of the middle of the ski
- Back tip width: Float of the back of the ski
- Radius: Float vs. pierce (if you plunge your ski through the snow, how easy is it to extract?)
- Height: Speed vs. turning (longer skis will increase speed and increase turning radius)
- Weight: Float & comfort on your legs & transport (light skis will increase your skiing endurance. Material will dictate how long they last)
- Camber / Rocker: Turning & speed (This helps with turning and drag. There are some fun models for demonstrating the effects of camber on a ski)
- Metal tip: Durability.
- Nucleus material: Flexibility & Strength & Weight.
- Stiffness: Control.