Well, standard infantry wore what they could afford. Whether they were extremely poor and had just the clothes on their back, or they were a somewhat rich farmer who could afford a hauberk, they wore what they had. Surcoats were mostly used by knights (who are far richer and noble than mere peasants) but if a peasant had the money, who was stopping him? :)
I feel it's fitting to mention that my army and Castle world is based off of what a 12th century world would look like. Meaning that the only helmets I use are the Nasal Helm, the Kettle helm, an (if I had any) the bullet helm. Granted the Great Helm was created around the end of the 12th century, my Castle world is during the early-to-mid 12th century. And for the torso with "only the surcoat" if you look under the newer versions (Kingdoms, but I believe the Crownie's surcoat had this too) you can see that they indeed are wearing chainmail underneath it. :)