Here's a quick rundown of the basic guns in Fallout 3 that you'll find in the first few levels. The "DPS" (damage per second) values are from the Wikia Fallout 3 Wiki weapon page and should be taken with a grain of salt. These assume 100% weapon condition, which is something you'll rarely find out in the wilds at early levels.

For sneak attacks, it may be better to use a weapon with high initial damage but slightly lower DPS.

There are almost always uniquely named versions of the basic weapons that do more damage or work better.

BB Gun (2H, Small Gun, 4 DMG, ~3 MDPS): While this doesn't do a lot of damage, it's a great weapon to use while escaping from the vault against radroaches. A sneak attack against a radroach will almost always be a one-shot kill.

10mm Pistol (1H, Small Gun, 9 DMG, ~17 MDPS): This does a heck of a lot more damage then the BB Gun and carries a 12-round clip. Ammo is fairly easy to find, but accuracy suffers at longer range. For the stealthy types, there's a silenced version that does slightly less damage but is totally silent. (Hint: Easily obtained in Megaton if you're a goody-goody type that's not squeamish about taking violent action to stop a foul plot.)

.32 Pistol (1H, Small Gun, 6 DMG, ~11 MDPS): An alternative to the 10mm pistol for smaller targets. However, since this uses the same ammo as a .32 hunting rifle, I strongly suggest that you stick with the 10mm pistol and save all .32 ammo for your rifle.

Chinese Pistol (10mm, 1H, Small Gun, 4 DMG, ~3 MDPS): These are pretty much junk weapons. There are better choices for using up precious 10mm ammo.

Hunting Rifle (.32, 2H, Small Gun, 25 DMG, ~17 MDPS): Once you find one of these, this or an assault rifle will probably be your two-handed weapon of choice up until level 8-12. It's an excellent weapon for mid-long range work with decent accuracy (0.3 spread vs 0.5 spread for the 10mm pistol). I always equip this when roaming the wastelands in case I run into trouble.

(R91) Assault Rifle (5.56mm, 2H, Small Gun, 8 DMG, ~32 MDPS): The damage number is misleading as usage in VATS always shoots (3) bullets for each queued action. This is a very devastating weapon in VATS and lets you mow through an area fairly quickly. Very useful in narrow confines or underground where most combat is at mid-range and you need sure kills.

Chinese Assault Rifle (5.56mm, 2H, Small Gun, 11 DMG, ~44 MDPS): Again, the damage number is misleading as VATS always shoots (3) bullets at a time. This is a fairly easy weapon to find early on as a natural offshoot of doing tasks for Moira in Megaton. The only downside is that you'll love it so much that finding 5.56mm ammo and enough caps to pay for repairs at vendors will become an obsession. My last repair bill for this was 499 caps after a long foray into the Marigold Metro Station complex. At higher levels, it's easy to find additional CARs that can be used to repair your primary CAR, but at low levels you'll be mostly paying vendors to repair it.

There are also a few weapons that I'm not going to give stats for:

Energy Weapons: I'm not a fan of energy weapons, so I don't use them. It's also harder to find ammo for these until later on.

Shotguns (excellent for close-in work): These are excellent close-in finishers, but horrid at medium/long range. The spread on shotguns is around 5-7 compared to 0.5 for a 10mm pistol. I'll carry one if I have it, but it will rarely see use as I prefer to keep my enemies at medium/long range.

Scoped weapons (Scoped .44 Magnum and the Sniper Rifle): Scoped weapons are very tricky to use. They don't work like scoped weapons in other FPS games where it's a dependable one-shot kill weapon. However, they are very accurate in VATS with a high critical damage multiplier. The primary use of scoped weapons in Fallout 3 is often as a poor man's binoculars. The .308 ammo for sniper rifles is also a bit sparse, so it's not a weapon that you're going to want to always use.

There are also the explosive weapons (grenades, mines) along with the really big weapons (missle / nuke launchers, chain-guns, etc). These are also special-purpose weapons that will probably not be the first thing you reach for until the later levels.

Updates:

I'd like to add the 10mm SMG (1H, Small Gun, 7 DMG, ~35 MDPS) as a very interesting weapon to replace your standard 10mm pistol. You'll probably find this around level 6-8 if you're exploring. In VATS mode, it shoots off 4 rounds at a time, but the accuracy is a lot lower then a 10mm pistol. Think of it as a one-handed assault rifle equivalent as it does about the same DPS and has similar accuracy.