The 10mm Pistol is perhaps one of the most common guns found in the Capital Wasteland, and as such it is a fairly practical weapon as repairs and ammunition are very easy to find. Given that this is the first weapon you get, you should be using it fairly often. It does the most damage of all conventional pistols, the ones which survived a nuclear war and 200 years of neglect, that is. Although you wasteland dwellers may be keen to pick up something bigger and generally more mean such as the Assault Rifle, there are several reasons why you should consider this weapon; as a side arm at least. The 10mm pistol weighs only 3 pounds, which will leave you free to carry more glorious loot! That's as good a reason as any; but if you need more, the large magazine (12 rounds), fast reload (clip fed), and small bullet spread means that even a child could put 12 rounds into a mutie's hide from about 50 yards.
And for all you 'sneaky-shooty wastelanders', if you're lucky you may even find a silenced version; those raider scum won't even know you were there! So PLEASE consider carrying a 10mm pistol with you: it might just save your life.