There are no references here to non-Real World weapons, such as the Demat Gun, among others. This greatly limits the articles scope, and halts just where we should have the most info. This page has way too many issues.
A firearm, commonly known as a "gun", was a term encompassing a variety of weapons which used a projectile fired from the weapon relying on chemical explosives to propel the projectile at high velocities from the firearm. In the words of Silurian scientist Bokka K'to, "It project[ed] a small piece of metal at high speed." (TV: Doctor Who and the Silurians) They were typically used to penetrate surfaces to maim or kill and were a favoured weapon of humans.
Firearms, as a relatively primitive technology, could be neutralised by more advanced technology. For example, Sontaran soldiers employed a cordolaine field that affected metals such as copper, causing weapons using copper casings on their projectiles not to fire. (TV: The Sontaran Stratagem / The Poison Sky)
UNIT and other military personnel usually used assault rifles and pistols. Officers usually carried pistols or revolvers. In future centuries future soldiers like the Anglican soldiers and soldiers in the Human-Hath War seem to carry a type of assault rifle.
An appreciation of the usefulness of firearms was not limited to humanity. Upon landing on the planet Exxilon a Dalek taskforce's weapons were rendered inoperable, forcing them to replace their energy weapons with semi-automatic ballistic weapons. (TV: Death to the Daleks)
The Master was surrounded by UNIT soldiers from all sides with rifles pointed at him when only one handgun was not sufficient to guard him. This was after he tried to escape capture by stealing Bessie and the Doctor remotely controlled her to drive back to him. (TV: The Dæmons)
Wilfred Mott took his old service revolver with him when he sought out the Tenth Doctor. He later gave it to the Doctor, who took it to use against the Master. The Doctor had to choose between shooting the Master or Rassilon, but finally chose to shoot the nuclear bolt, destroying it and breaking the link that anchored the Time Lords in the present time, sending them back into the Time War and saving the universe. (TV: The End of Time)
The Fifth Doctor used a handgun against a Dalek mutant that had escaped from its damaged armour. He decided that he needed to kill Davros but when the moment came he couldn't bring himself to pull the trigger. (TV: Resurrection of the Daleks)
After the Twelfth Doctor returned to Gallifrey, Rassilon's firing squad were ordered to shoot him, but purposefully missed. They then sided with the Doctor, dropping their guns and standing at his side. Last to join him was the General who dropped his pistol after telling Rassilon "Lord President, with respect, get off his planet." Desperate to save Clara Oswald, the Doctor stole the General's gun and threatened him with it. The General told him it was the side arm of the Personal Guard of the Lord President and had no stun setting. After making sure the General could still regenerate, the Doctor shot him in the chest and fled with Clara. The General then regenerated into a woman, his preferred form. (TV: Hell Bent)
Behind the scenes
Most firearms used in the 2005 series are of Heckler & Koch manufacture, specifically G36 assault rifles and USP sidearms. Glocks and Webleys have also been used.