Knife:
This is an item that both characters have by default. In my opinion, it isn't terribly effective. But, if you run out of ammunition, at least you know you have something there...

Beretta:
The beretta is the standard handgun. Jill has it by default, Chris will have to go find Jill's gun. And yes, it is Jill's gun, because when you find it in the Main Hall of the Mansion Chris says that it's Jill's gun. This gun will be very useful against many enemies in the game, and it's the one that you most commonly find ammunition for.

Shotgun:
The Shotgun is found in one of two different places. In the normal game it's in a study beyond a room with a trap in it. Jill can just go grab it, because Barry will save her. Chris will have to find the Broken Shotgun to obtain this item. When you play Arrange Mode both the Broken Shotgun, and Shotgun have changed location. This gun is very useful against more powerful enemies.

Bazooka:
This was Forest Speyer's gun, and Jill is the only one who finds it. It's essentially the same thing as a Grenade Launcher, and it is very useful for the more powerful enemies of the game. It is what makes Jill's game much easier, since she has it in time for more powerful enemies, whereas Chris has only the Shotgun to work with... The Bazooka has three different types of ammunition: Normal, Acid, and Flame. Flame is good for Spiders, and insects (Chimeras), and the Acid is good against quite a few bosses, and Hunters.

Colt Python:
The Colt Python is the Magnum that you find in the Mansion. You find it when you return to the Mansion, and because of it's location, Chris will encounter Hunters before he even has a chance to get at it. Jill has the same problem, but unlike Chris, she has the Bazooka. The Colt Python changes location in Arrange Mode, and it is found in the Storage Room, in the gun display case (where you normally would find the Broken Shotgun). This means in Arrange Mode you find it very early on in the game, and thus have it long before you encounter the Hunters.

Rocket Launcher:
You will only find this weapon at the very end of the game. When you have done enough damage to the final Tyrant, Brad will drop it down to you. It takes a long time to load, but it will kill the Tyrant with the first successful shot you get off. You can also obtain an unlimited Rocket Launcher, but it's very complicated and difficult to do, and I really never have been able to accomplish it. Besides... I prefer the Unlimited Colt Python. ; )