tha
just try and get the biggest sprocket you can on the back..you may have to change to a long cage derailleur in order to do this...alternatively get a compact chainset 50/34
On road bikes its either Short (SS) or Medium (GS), most of the new GS RD's will do upto 30-32th,
@User9609 I think you may find I wasn't advocating it as the sole answer, just as something else to add to it for that little bit extra beyond actually changing the chainset,
I pointed out changing the chainset to a compact chainset so you can fit smaller rings than a 38th would require moving the FD down, a skill many don't have (though it is quite easy), one option would be to fit a compact with a 36/52, you wouldn't then need to change the FD and like a compact would require two new chainrings.
I personally find the change of 16th on the front quite large its in the order of 45% which depending on the cassette could mean shifting several gears to be in the same range.
I ride a compact triple, which gives me a wide variety of gearing options, again something lacking in a compact double (a compact chainset is determined by its BCD not its chain rings)
The new 11sp shimano can fit both a 34/50 or a 39/52 or a variation
As a side not, I was actually quicker on the setup of a 30/40/52 and a 12-27 than I am on my current 28/38/50 12-23, but I prefer the latter, even had it set up with a 26th inner (and 38/50), but that posed the same problems in large rear gear shifts, on the 12-27 it gave me however a 25-110" range.
If you are looking for range a triple is the only real answer, as it gives a good double with a close front with gearing for hills, however I keep reading about how people want to have a low gear on a double which usually is really only available as a 34/50 and even a 34x34 only manages to give a 26" ( I would need to check) but not many road bike setups will do that, and then you have to compromise on ratios, where as I have a 12-13-14-15-16-17-18-19-21-23 with the 28/38/50 and have a 33-110" range, which I can change to the lower gearing if its needed (but not round here), and I notice every single shift even though some a very subtle.