I partly agree with djaustin, stem wise less so, IMO stem length on a road bike has much more to do with fit than steering/handling, were as on a MTB is almost the other way round. But if you look at guys like Cavendish, Gilbert, Cancellara, most of peloton in fact e.c.t they all use 140mm stems. Boonen, even when he had a custom frame made up for him by specialized, he still used a 140mm stem. I doubt that they would do that if it was going to handle like a barge. On the road you don't "steer" quite in the same way as you do off road...if that makes any sense...probably not!
Anyway back to the OP's question I would say that the medium will be too small, you could probably get it to "fit" sort of but I think you would regret it. I have just bought a second hand boardman road frame, a large; I am a bit taller than you at 6'1-ish but the same leg measurement, I would say I was on the upper limit size wise, so think a large would be prefect for you.