Lots here with back problems- me included- but not when I am riding the road bike. The stretched out position of it just takes the strain off the back and I am OK.
Hand and neck pain is a problem with fit- or your riding style. It does not always mean raising the bars though. My most comfortable road bike is the one with the bars 3" below the saddle. No Back- or hand pain and I cured the neck ache by taking the peak off my helmet.
That is my conclusion for my body on my bikes but you and others may find different.
On the tyres- fitting a wider tyre will make the ride more comfortable. they will absorb road shock better and they can be run at a lower pressure and still not get pinch flats.
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How long was I in the army? Five foot seven.
Spike Milligan