Fallout Weapons Guide: One-Handed Normal Weapons
by Mazca

10mm Pistol
You start with this gun, and it really is not worth keeping once you get the submachine gun. It can fire only in single-shot mode, and hits from it rarely do more than the stated 5-12 damage, even to unarmoured targets. You will appropriate an SMG very near the beginning (in Vault 15), so after that sell this gun to the first person with enough money - It's dead weight.

10mm SMG (Submachine Gun)
The first good weapon you will encounter. Found in a locker on the bottom floor of Vault 15, this combines the same single-shot power (5-12) as the Colt .45, but at the same time has an excellent 'Burst Mode'. This can kill most people with anything less than Combat Armor in one shot if you are nearby, resulting a very gory but satisfying death - often their entire chest will be ripped open or their head and arms blown off. Fun. It's worth keeping until you get the assault rifle (which pretty much supersedes it in every way).

Tips
If you are shooting somebody from medium to long range (more than about 6 hexagons away from you) don't use burst mode unless they are standing in a tightly-packed group of other enemies. Only one or two of the bullets in the 10-shot burst will hit them and you will have wasted a lot of ammunition. Instead, use the weaker but more ammo-conscious targeted single-shot mode.

Desert Eagle .44
If you have space and can find enough ammo, this gun is worth having. It has no burst mode but the single-shot power and accuracy are significantly superior to the 10mm or SMG. It's not a must-have though.

Other Pistols
There are plenty of other pistols around, such as the .45 and a .223. However, none are particularly amazing - see the Desert Eagle.