I think you’d like a boot such as the Rossignol BC X11 ($280). They’re a hiking boot in ski-boot guise, with stiff plastic uppers, a great fit, good for kick-and-glide but stiff enough for turning on the downhills.
Take a look as well at Salomon’s X-ADV 5 ($160). A little softer than the Rossignols, so better for travel on rolling rather than steep terrain. But comfortable and warm. Similar in weight and performance is Alpina's BC 1550 ($170). Insulated, with a plastic cuff around the ankles for support.
Speaking broadly, skis versus snowshoes for backcountry use can be argued several ways. Snowshoes are easier to use, better in rough terrain, compatible with any boots. Skiing is definitely faster overall because of the greater speed on the downhill. But…it can be more difficult to manage, more specialized, and not so maneuverable on steep or varied terrain. I’ve done both snowshoes and skis for backcountry use. I like both, but it depends on what the trip is like.
But, for skiing, you definitely need the right gear: ski boots, skis with bindings, and so on. I think you’ll have fun with it!