I just recently did this same thing (and in Craftsman style no less!).
We ended up doing a mix of MDF and hardwood.
We used hardwoods in areas where water, or moisture & wear would be an issue. For example, the baseboards in the bathrooms, and the laundry room, are all hardwood, as are the window sills. We also used hardwood in areas that take a beating, like the risers & skirt boards on the stairs.
MDF isn't the best where it can get wet, but all hardwoods can get expensive fast. So this mix worked out well for us. We painted all the millwork, so the hardwoods were of affordable variety (poplar).
In areas where moisture isn't an issue, MDF works just fine. Once it's on, and painted, no one knows what it is anyway.