All-mountain boots are exactly what you need for that mix. They're designed to handle groomed runs, moguls, and light off-piste terrain without excelling at any one thing—but that's the point. Think of them as the Swiss Army knife of ski boots: comfortable enough for a full day on the hill, responsive enough for advanced skiing, and forgiving enough that you won't be fighting your equipment.
The trade-off is that they lack the extreme specialization of other boot types. They won't give you the razor-sharp edge control of a frontside boot for high-speed carving, or the walk mode and uphill capability of a freeride boot for deeper backcountry missions. But for most resort skiers who explore different terrain, that versatility is a feature, not a flaw.
A good rule of thumb: if you spend 70% or more of your time skiing inbounds at the resort and dabble in different terrain, all-mountain boots are your best bet. Only consider a specialized boot if you're consistently spending the majority of your time in one specific discipline.