Bad backs are not what will denote what style of bike you get. I have a back problem and when I went road after 16 years on MTBs- I chose a road bike with a fairly relaxed riding position. Short top tube and bars just below the saddle. I could not ride any length of time in the drop position-and I am talking 10 seconds and my back was screaming. Got a high rise stem to bring the bars up to saddle height and it was no better. 6 months later and I decided to "Practice" that drop position. 20 seconds at a time on a straight bit of road and I would force myself into the drops. 1 month later and the drop position was comfortable. Next bike was a Race geometry bike with a longer top tube and the bars 4" below the saddle. I still ride on the hoods (On the brake levers) most of the time but into a headwind- Going downhill or if I want to catch the rider in front and the drop position is comfortable. That long low body stance seems to help my back.



The black bike is the relaxed Geometry bike and you can see the height of the bars in relation to the saddle. Typical older rider configuration.

But the bike that is comfortable is the Boreas- and that includes long road rides up to a metric. Above the metric and I use a bike that is similarly set up to Boreas but with a triple Crank.