The ideal bike for you would be touring bike, but those are very rare now. Second choice would be a women's sized road bike: when you're going 15+ miles you don't want a hybrid or mtn bike. You can put mtn gearing on a road bike. Your LBS should do it for free. Just don't get a compact double, you'll want a triple and make sure you have the option of later adding either a bike rack or panniers. Not all bikes will allow this.