Living, dining and hallway areas - Laminate - assuming a hardwood look - seems ideal for your situation. You can put the laminate down and soften it up with inexpensive area rugs. There are some beautiful area rugs to choose from. When the rugs get dirty, it is not nearly as expensive or time consuming to replace as taking out wall to wall carpet. Just roll up the old rug, and replace it with a new one. Also, what I find is that we don't walk in the perimeter of a room, so the rug would protect the most used portion of the laminate. You get the best of both worlds.
That would probably work for the hall, too, and, again, if it gets dirty, roll it up and replace it.
Steps perhaps use laminate and a pretty stair runner carpet over the center would work. Most of us only use the center of a stair, so I don't think that you would have to worry too much about sand, grit, and rough family usage with a stair runner in place.
With area rugs, make sure to secure them in place with double sticky tape.