Basic Weapons - There are numerous basic melee weapons in Fallout 3 including the Pool Cue, Police Baton, Rolling Pin, Knife, Tire Iron, and Nailboard. All of these weapons are useful if you have nothing else at hand. Because you can pick up the Baseball Bat - which is superior to all of these weapons - before you even leave Vault 101, all of these basic weapons are mostly useless. They also have a very low value to merchants.
Baseball Bat: DPS 12- You can pick this up early in Vault 101, and it is a reasonably effective basic melee weapon with a DMG rating of 9. It is not a quick weapon however, and will probably be quickly discarded in favor of other better melee weapons. It has very little value to merchants.
Combat Knife: DPS 20 - Although the combat knife does less damage per hit than the Baseball Bat, it is quicker and can do more damage over time. It also has a much better crit chance than normal (3x) and does more damage when it does crit, so this weapon is good choice in the early game.
Lead Pipe: DPS 20 - This weapon does the same damage per hit as the Baseball Bat, but it can be swung quicker which results in more damage over time. The Lead Pipe is not a remarkable weapon otherwise.
Chinese Officer's Sword: DPS 23 - This weapon is a true sword, which looks very cool, but it does less damage than you might expect. It can be swung with reasonable speed, has a slightly better than normal crit chance, and does a fair amount of damage when it does crit. It is a good choice until you get a hold of a Sledgehammer.
Sledgehammer/Super Sledge: DPS 30/37 - This is when melee weapons start to get fairly serious. Both of these weapons put down a good amount of hurt, have good crit damage bonuses, but don't crit more often than any other weapon. You can get these weapons fairly early on by defeating a Super Mutant equipped with one. Once you do get one, you'll likely keep hold of it throughout much of the game. They are very heavy, so they make poor loot as a result.
Ripper: DPS 30 - The Ripper is a very powerful and surprisingly cheap melee weapon which, while rare to see on other characters, will show up frequently at the gun shop in Rivet City once you get around level 10. Unlike other melee weapons, simply pressing the attach button and holding it will cause this weapon to constantly put out damage. Despite being obviously mechanical, you don't need any sort of power source to operate it. This is the best basic melee weapon, but it is overshadowed by some uniques and by the Shishkebab, and you'll like run across one of those other weapons before you get your hands on a Ripper.
Shishkebab: DPS 80/120 - The most powerful melee weapon in the game, the Shishkebab is a schematic-built combination of a flamethrower and a sword. It does a ton of damage and attacks very quickly. This damage is increased to the point of absurdity when it is combined with the Pyromanaic perk, which increases damage done by this weapon by 50%. Keep in mind that since this is a fire-based weapon, so it will set off gas leaks. And unlike other fire-based weapons, this will set off a gas leak merely by having the weapon drawn!