What would be the best weapon to go against each of the Prometheans, and what would be a go-to weapon on legendary solo?
Depends on the situation.
To be honest, if there are Promethean weapons, use them. Don’t underestimate the Suppressor and the Light Rifle, and don’t waste their ammo on say, Crawlers. The Promethean power weapons, obviously, are ridiculously helpful. However, I’d always choose a Light Rifle over a Binary Rifle. Scattershot, Incineration, (when you find them 
by all means.
Keep a dmr/br/carbine/light rifle around for watchers and crawlers. They’re good against knights too.
When you need to take out multiple knights, keep a powerful weapon around for your secondary. Any power weapon will do. On legendary, weapons like the railgun and binary rifle may not kill in one hit. To save ammo, hit them first with the power weapon then follow up with some headshots with your standard rifle.
A good old melee from behind takes care of many knights in the game while they are in the middle of teleporting in.
So lets say you start out with the standard loadout. Assault Rifle + Pistol.
Try to take the Knights out as fast as possible by luring them away solo. Speaking from experience on levels like Requiem/Infinity, shoot first, jump back and keep repeating until you two can have some alone time. And by alone time, I mean unloading a clip or two with the AR. Don’t be afraid to Melee once you get a chance. After you break the shield would be prime time. Hopefully they drop a Scattershot, Lightrifle, Binary Rifle, Incineration Cannon. Sometimes you get stuck with a Boltshot drop, but that works too. Use the initial Knights weapon against the other Knights, keeping in mind not to get into a dogfight with two or more. Lure them off one by one.
Crawlers can easily be picked off with a shot to the face from a Pistol, Battle Rifle, pretty much any precision weapon. Or just a melee to the face if there are only a couple.
Watchers… freaking Watchers… use caution cause they will trick you into turning your back. Pick them off with a precision weapon. If they run, and you are surrounded by Crawlers/Knights, pick off the crawlers and knights, then get the Watcher. They won’t respawn crawlers, and you’ll know if they are trying to respawn a knight, so you can chase them off again.
TL;DR:
Knights - Rocket Launcher, Sticky Launcher, Shotgun, Scattershot, Assault Rifle, Suppressor, Plasma Grenades - In that order
Crawler - Precision Weapon TO THE FACE
Watcher - Precision Weapon TO THE FACE
Suppresor the shield, then headshot them/keep suppressoring them.
Works like a charm.
Use the scattershot whenever you possibly can.
Don’t underestimate the auto-sentry - it’s hugely helpful on Legendary. It helps distract and clean up areas where there are multiple enemies, and also helps to chip away at a Knight’s shields. Grab it whenever you can, it’s far better than hologram.
plasma pistol and dmr is all you need in this game
> What would be the best weapon to go against each of the Prometheans, and what would be a go-to weapon on legendary solo?
Plasma Pistol in general is your best friend + any precision Weapon, but the covie carbine seems a little too weak for anything other than covenant. Rapid firing the plasma pistol is often much more useful than a charged bolt.
The suppressor, any power weapons.
Shotguns are useful but almost useless at close-mid range.
The thing you have to keep in mind about knights is their shields are just a bit more resilient than an elites and charge much faster but once that comes off, a headshot will do them in. Watchers, then crawlers, then knights. They can take a ton of body shots so your priorities should be taking the shield out and popping headshots, but I can’t put enough emphasis on widdling down the shield.
Don’t Rely on using power weapons to take out a Knight when it has full shields, you’re just going to waste the ammo and have more knights to take care of. Instead, use it to clean up leftovers once shields are gone.
Designate one precision weapon (LR, BR, DMR) and use your other weapon slot for exchanges focused on Plasma, Automatics, and Power weapons. the needler works wonders too.