Two pieces of Doom that pull the whole game together are the demons and the weapons with which to kill them. Some of these creatures are so recognized that even non-doom players will see them and immediately know where they're from. I'm not going to set up and name every monster and weapon, but there are so many standouts, it'll seem like it.
The Imp is one of the most recognized small demons in the game. They throw fireballs that do a lot of damage compared to most of the weaker enemies. They can be dangerous in groups but they also aren't the tankiest of the bunch. Shotguns do a good job of taking them down. If there's a group, a super shotgun is a good answer.
The pinky is officially just named "Demon" but retroactively are just called "pinky", thanks to the standard culture. They only do melee attacks to bite you but they do have a translucent twin called the Spectre. Thanks to their close ranged nature, they are generally taken down with the chainsaw rather easily.
The Cacodemon is arguably the most recognized demons in the entire game. Their red blobbish nature and quick attack missiles make them very noticeable. A super shotgun and chaingun are good ways to take them down.
The Barons of Hell were first seen in the last level of Knee Deep in the Dead and have since been considered a staple of Doom lore. Barons hit hard and can take a lot of punishment. The best answer to them, especially multiples of them, is the plasma rifle. If you run out of plasma rounds, get them with the Super Shotgun and/or the rocket launcher if you're at a safe distance.
The last of the demon minions is the Archvile. Making their debut in Doom 2, they are obviously in the game to drastically increase difficulty. They tank about as much as a mancubus, deal more damage overall and bring monster bodies back to life. They are priority targets and deserve your top plasma ammunition from either the plasma gun or the BFG 9000.
The BFG 9000 has been one of the iconic weapons in this entire franchise. One shot can take a multitude of small demons down while also doing tremendous damage to larger targets. If you have this gun, many of your problems will be dealt with by melting them into sludge. The big drawback is that it's slow to fire and takes up 40 plasma cells per blast. Use it when you absolutely need to.
The boss demons, namely the Cyberdemon and Spider Mastermind are prime BFG 9000 targets. The Cyberdemon can easily down you in one to two hits with his rocket attack. The Spider Mastermind fires a chaingun and each shot is the damage equivalent to a shotgun shell. Overall, the Cyberdemon is the more challenging but the Mastermind can also drain your life very quickly if you are not careful. Your best bet on both of them is to use your big guns and hide behind cover to avoid their wrath!
Last but most certainly not least, a weapon you can use on anything up close, the Super Shotgun. This is the king of shotguns. I don't care what anyone else says about other shotguns from other games, this gun gets it done! If all else fails, if you have two shells you can shoot, this could take care of whatever is after you. The spread is huge and very concentrated. You could take down three or four smaller opponents in one shot if they're close enough together. It is a gun that lives up to the name and sets the bar high for any other shotgun.