There are quite a few weapons in Apex Legends out there, so it can be a little overwhelming when jumping into the game for the first time to figure out which weapons you want to pick up, and which ones you want to leave behind. At the end of the day, most weapon choices are going to come down to personal preference; a weapon you're comfortable with and hit your shots with consistently is going to work out better for you than a weapon that might have a higher DPS (Damage Per Second) but that you find difficult to use.
This list is separated in tiers, and ranked in a mix of what is mathematically the best stat-wise, and what I've found works the best in my (embarrassingly extensive) time in the game:
Coming in first on the list as a surprise to absolutely no one is the Mastiff. Only available from Supply Drops, the Mastiff is quite frankly capable of a ludicrous display of violence. The highest DPS shotgun in the game, the Mastiff's both the easiest to use and most powerful close-range weapon in the game.
Another shotgun on the top of the tier list. The Peacekeeper is outclassed in close-range only by the Mastiff in terms of DPS. It's a little more difficult to use considering the tighter projectile spread, but if you hit your shots, the Peacekeeper is a frightening weapon to fight against. For maximum effectiveness, pair it up with a Precision Choke and charge the weapon up.
The Wingman is, quite possibly, the most versatile weapon in the game, capable of being a force to be feared both in the closer mid-range and long-range, as well.
It has an impressive damage per shot in relation to its fire rate, and if you manage to attach a Skullpiercer Rifling, headshots are going to absolutely shatter your enemies.
I have the Devotion placed one tier higher on my list than most other lists that I've seen, and it's because there have been many, many fights that I've won with this weapon that I know for a fact I could not have won with any other weapon in the game. Sure, the charge up time for the weapon can be rough, but if you start pre-firing as you turn a corner, wiping an entire team with one magazine with the Devotion is easier than you'd think. Just be sure to stock up on Energy Ammo or be willing to trade the weapon for another when you run out.
The R-301 Carbine has an absolutely incredible DPS, and the only reason it isn't ranked ahead of the Devotion is because of the magazine size. The R-301 almost requires an Extended Magazine to maximize its capabilities; without it, you can't afford to miss shots. If you can manage to maximize the production, there are few weapons that can rival this one.
The Spitfire is an LMG, and because of that, comes with a hefty Magazine size. This weapon has a serviceable DPS, and combined with the sustained fire it's capable of, makes it a really solid weapon. Outnumbered engagements are made a lot easier when you don't have to reload between targets.
I have the G7 Scout ranked above the Longbow, but it wasn't an easy choice. In the end, it came down to ease of use.
The G7 Scout is a great weapon for mid-range and long-range, and its sustained fire capabilities compared to the Longbow make it capable of keeping you in the fight even if you miss a couple shots.
This one was tough. The Kraber has the highest damage per shot capability in the game, and it really isn't even close. The Kraber is capable of one-shotting with a headshot just about anybody in the game, the problem is that you get a very limited ammo supply, and the scope zoom means it is not viable inside a certain range. But, if you're capable of limiting engagements to this weapons strengths, you can't be beaten.
The Flatline is another solid choice of Assault Rifle, ranked below the R-301 just because of DPS. It has a bit of a lower rate of fire but a couple more shots in the magazine, so you should spend a little less time reloading with this one; the trade-off being you'll see a noticeably slower time-to-kill.
If you can't get your hands on a Kraber, then the Longbow is the next best choice. It's nowhere near as powerful as the Kraber, but it has a significantly faster rate of fire, making follow-up shots a lot easier. It'll be very rare that you can one-shot someone with the Longbow, but if you can get your hands on a Skullpiercer Rifling, it's certainly possible.
The Hemlok is, in my opinion, one of the best options for mid-range engagements. The burst-fire is pretty easy to keep tightly packed, and getting a full burst on somebody, especially if you manage one or two headshots, is debilitating.
Land three full bursts and your target is likely down. But, the burst-fire makes it a highly-limited weapon, not having the DPS to keep up in close-range, and difficult to land shots within long-range.
The R-99 is the highest DPS Sub-Machine Gun in the game, beating both the Alternator and the Prowler. It's also, in my opinion, the easiest to use of all of them, with a slightly higher magazine size than the Alternator, and being full-auto instead of burst-fire like the (default) Prowler. For close-up, if you can't get your hands on a Peacekeeper or R-301, this is a good choice.
The newest weapon on the list, the Havoc is the third weapon that uses Energy Ammo. Think of it as a lesser Devotion; less DPS, less ammo in a magazine, but with a similar charge-up style.
Attaching a Selectfire Receiver enables you to fire in one concentrated shot instead of full-auto, using five ammo per shot instead of one.
The Prowler is the only Heavy Ammo Sub-Machine Gun in the game, and by default, fires in five-round bursts instead of full auto, giving you four trigger-pulls per magazine. This can be changed with a Selectfire-Reciever and makes the weapon a bit easier to use. This is a decent early-game choice if you need to jump into the fray immediately, but the longer the match goes, the less reason there is to keep this weapon around.
The EVA-8 Auto is the only auto-shotgun in the game, and some have argued that it's better than the Peacekeeper, but I just don't see it. It's much harder to optimize your damage output with the EVA as compared to the Peacekeeper since the EVA seems to have a harsher spread, and the inability to attach a Precision Choke means your range is going to be significantly handicapped, putting you at a distinct disadvantage against a Peacekeeper user.
The Alternator is a weapon that you're likely to see a lot in engagements right after landing, and for good reason; if the enemy doesn't have armor yet, rushing them with an Alternator is typically an easy win. But, much like with the Prowler, the later the match gets, the less reason there is to keep this weapon around.
The RE-45 is going to get outperformed by most other close-range weapons in the game, but if you can manage to keep your shots on target and especially on the head, it's not a bad little gun. You're going to spend a lot of time reloading even if you have an Extended Magazine, and there's little reason to keep it over any Sub-Machine Gun.
Try as I may to like this weapon, I just can't make it work. There have been some times where I've won engagements with it, and it does make for an interesting weapon capable of performing decently at any range.
It's pretty easy to hit shots no matter where an enemy is, but it seems to get outperformed by weapons that specialize; it's simultaneously the second-worst shotgun in the game, and the worst sniper-rifle in the game. Attaching a Precision Choke alleviates this somewhat, but the inability to attach an Extended Mag cements this weapon's spot down here, in my opinion.
This weapon is nearly useless. The only time you're going to win an engagement with someone of similar skill to you is if they're using a Mozambique and are quite a ways away, or you just happen to have great armor and they don't.
It's tough to say which is worse between this and the P2020; on the one hand, the P2020 can perform at a range further away than hugging distance, but on the other hand, Mozambique has a significantly higher DPS, provided you can stay close enough and hit all three shots.
Either way, we both know you'll be trading them out the moment you get the chance.