Some thinking says if you've got back problems comfort shouldnt be important.
The argument is the the cushioning in the shoes stops your body correctly reacting to the impact of running. Allowing the shock to run though your lower limbs and actually causes more impact futher up in your knees/pelvis/back.
This all might be rubbish but its probably true if you tried to run on concrete barefooted you'd probably have very sore feet, ankles and calves.
Personally again I'm not really sure about this advice
"to find whether you are flat footed or the opposite"
If you go and get a gait analysis before you've started running there bound to find a problem. If you havent done much running in years the muscles round your ankles and calves are going to be weak meaning your'll run badly.
Like all things there is some skill to running and surely it would make sense to do some running first to improve your technique. Then get a gait analysis if your having problems.
Although there does all of a sudden seem to be a lot of marketing BS about barefoot running I do think there is something in it. But you dont need any fancy trainers you just need standard pair with a thin sole, like squash shoes.