The Doctor almost never seems to carry / use a gun and I've heard that this is a deliberate decision on the part of the writers; that this is somehow part of The Doctor's character.
All I can find about this is (from the TARDIS wiki):
One practical limit on the use of firearms was that they were usually lethal. While it was possible to use a firearm to incapacitate rather than kill, this could be done only by inflicting serious injury and pain. While there were forms of ammunition known as "less than lethal" intended for incapacitation, such as rubber bullets, they still inflicted great pain, and were lethal under certain circumstances. For this reason, individuals such as the Doctor and Sarah Jane Smith often refused to use them on moral grounds.
This page also lists the occasions where The Doctor does use a firearm.
But aren't these the exceptions? Isn't there a(n unwritten) rule that The Doctor almost never uses a handgun? I'm looking for both an in- and out-of-universe explanation, if they exist.