Frame size is the vital starting point, but if you're developing back problems, it would be well worth your while getting some advice on a good bike setup for your height, fitness and use.
A lot of "bike fit" salespeople are full of you-know-what but if you have a long- standing shop in the vicinity who deal with touring and commuting, i'd suggest you drop in for a chat,
even offer to pay for an advice session if you're not buying anything off them.
It will be money well spent, believe me.
Consider the cost of your commute on public transport.
Add to that gym membership, or a weekly physio session!
