One of the things that made DOOM famous was its interesting variety of weapons. Here in some detail is the weapons of DOOM. (Note: The Super Shotgun didn't arrive until DOOM II.)
FIST- Not much good unless you have a Berserk power-up. You're better off with the Pistol or the Chainsaw.
CHAINSAW-Better overall than the Pistol or Fist (Unless you have Berserk Mode), the Chainsaw is an excellent close-range weapon, which inflicts "chain damage" to your enemies, so that most can't attack you while you chop them to bits. You just can't beat the sound and humour of the Chainsaw. 'Nuff said.
PISTOL- Only really effective for Former Humans, Former Sergeants, and exploding those pesky barrels. Save your bullets for the Chaingun.
SHOTGUN- One of your best all-around weapons. Packs a heavy punch at close range, but only a slight pelting from a distance.
COMBAT SHOTGUN (AKA "SUPER SHOTGUN")- The bad-ass, double-barrelled, sawed-off relative to the Shotgun. Most people think it's along the lines of 'Shotgun x 2', when it's more like 'Shotgun x 3½'. More powerful, but takes longer to reload, and eats up two shells with each blast.
CHAINGUN- A nice weapon that directs heavy firepower into your enemies. The only good use for your bullets, really.
ROCKET LAUNCHER- Delivers an explosive rocket that makes short work of several enemies. Don't get too close to your target though- do so and you'll get toasted!
PLASMA RIFLE- A really fast-firing weapon that uses plasma energy to fry some demon asses! Uses up cells awfully quick though, so watch out. Unless you absolutely have to, save your cells for the good ol' BFG 9000.
THE BFG- Known to long-time DOOMHeads as the "Big F***ing Gun". Dishes out massive amounts of damage, but only to enemies in your line of sight. Uses a whopping 40 energy cells when fired, and when fired, takes about 1.5 seconds to discharge its deadly projectile.