Over the years, we've gradually changed my sister's "tundra tires" to thinner and thinner tires with less tread. It was a stability and comfort issue at first, but now she enjoys the increased speed.

I agree--I'd go with the tires first. Rims second.

Everyone's neck & back pain are unique. However, I rode a hybrid because I didn't think I could handle the road bike. SO, we bought a $50 road bike off of Craig's List and I discovered it was actually more comfortable. (The upright position of the hybrid can actually be more jarring on your back).