Every class shares a level; it is not split between individual soldiers.
This means, every time you unlock a new class, race, or gender, you're only starting from level 1 if you've never played as them before.
A lot of this is dependent on class. As a Vanguard for example, you'll probably never want to use an Assault Rifle - they're just too heavy, and as a Soldier, you'll usually give SMG's a pass - everything they can do an AR does better. Meanwhile, an Infiltrator gets lots of bonuses when using their trusty Sniper Rifle, evening if irresponsibly shooting it from the hip.
The second consideration is range: at very long ranges, a Sniper Rifle offers top notch accuracy. AR's and Pistols Can be pretty good. SMG's can be flaky though, and shotguns are nigh useless. By contrast, Shotgubs ate devastating at short range, but the loss of peripheral vision while looking down that sniper scope can get you killed.
The next consideration is the defenses of your opponents. Slow firing, high caliber weapons like Sniper Rifles and Pistols chew through Armor, but are weak against Biotic Barriers and Shields. Rapid fire weapons with a lot of projectiles, by contrast, like SMG's and Shotguns chew up Shields and Barriers quickly, but have trouble with armor. Assault Rufles are a bit of an odd duck as they're 'pretty good' at handling everything.
Additionally there are mods availiable for several weapon types that alter their capabilities. You can add Armor-penetration to an SMG or a shotgun, or a melee upgrade to a pistol or shotgun. Maybe a scope on your SMG to improve its mid-long range performance?
Finally, you may want to pair some weapons up with certain specialty ammo. For instance, SMG's are devestating in combination with Cryo or Incendiary Ammo as their high rate of fire gives them more opportunities to proc the special effects provided by these ammo types than, say, a slow firing shotgun.
Best Answer
Infiltrators: The Black Widow is easily the best choice for any Infiltrator and really the only weapon you will need as having this weapon without any capacity increases or weapon weight decreases and no upgrades will put in the negative for power recharge. Using the Viper is a second best when it comes to semi-automatic sniper rifles, although it is much lighter than the Black Widow, allowing for use of a second weapon without a huge effect on your power recharge. I, myself, prefer the M-3 Predator or a heavier option, if specced for more weight capacity in Fitness, is the M-6 Carnifex, which is a sniper/pistol hybrid in my opinion. For beginners, I would suggest going with the Mantis Sniper Rifle and the M-3 Predator. Making sure your Tactical Cloak is available at least once every reload is incredibly important for both semi-automatic and bolt action rifles, so packing as light as possible is a great idea.
Adepts: This class is reliant on your biotics more than your weapons but of course, it doesn't hurt to have as much as you can carry without hurting your cooldown reduction to give you an advantage, especially for difficulties like silver and gold. I would suggest making sure you spec into more weight capacity in fitness allowing you to carry a couple light weapons without affecting your power recharge. I personally use the M-3 Predator with the M-12 Locust (in combination with the Ultralight mod on the SMG). This allows me to have 2 weapons without decreasing my power recharge at all and it stays capped at 200%. So having a weapon on you that doesn't decrease your power recharge and is good for close to mid range is the perfect choice. You could even try the Disciple shotgun as it is the lightest of all the shotguns and is fairly decent. Otherwise, for beginners, I would stick with either using just the M-3 Predator or the M-4 Shuriken.
Vanguards: The Vanguards are heavy biotic players as well, as they have no real use for weapons in a firefight, though, obviously, having a sidearm or two is always useful in situations. Playing a vanguard, I found myself constantly switching to use a Shotgun, preferably the Disciple. I find myself occasionally popping off a round or two into the crowds of flying troops, but really only to finish of the couple of guys who tend to just barely survive my ensuing waves of destruction. Having watched many a Vanguard play, I have noticed lots of them prefer the use of a pistol, as you can quickly dish out head shots between Charges and Novas. However, I prefer to not be a in a team with a skilled Vanguard while playing an Infiltrator, as my targets tend to sprout wings and fly through the air like little ragdolls. For beginners, I would suggest the Katana or Predator.
Engineers: The Engineers are another class that really only use their weapons as a back up. I found myself constantly behind cover throwing out drones/turrets and a multitude of damaging tech powers in the direction of my foes. On occasion, I would end up with a guy sneaking up behind me, and I would have to throw a tech power, only to notice that another of his friends was next to him and my handy shotgun was ready to expel a shell into his chest. For this class, I would suggest a shotgun as well, though any weapon will do in all honesty, because if you are using it more than your tech powers, then you are probably doing very badly. I would only suggest carrying one weapon though, either a light assault rifle/shotgun or a SMG/pistol. Never more than one weapon is needed, as your tech skills will do the talking. For beginners, I would suggest the Shuriken or Predator.
Soldiers: These guys are great because they can pretty much use any weapon combination and excel with it. I would find something that definitely works for you and stick with it. What I like to use though is the Raptor sniper rifle and the Falcon assault rifle. The sniper allows me to lay down plenty of fire with its high magazine capacity and low recoil and still do plenty of damage at long range. The Falcon gives me a little bit of control when groups of enemies are in front of me. The Falcon is more of a grenade launcher on steroids then an assault rifle, as it propels its grenades a long distance and needs very little compensation when aiming above the enemy. Not only this, but it does a decent amount of AoE damage to enemies the grenade hits and staggers almost every troop you come across. You can also bounce the grenades off walls to hit enemies behind cover. Another great thing about Soldiers is your recharge rate on your powers isn't life or death or going to change the tide of battle, so having two heavy weapons won't make you better or worse then someone with a heavy and light or two light weapons. For beginners, I would suggest the Mantis sniper rifle and the Avenger assault rifle.
Sentinels: These guys are tanks. They have no real purpose other than to take all the hits for everyone, as they have a lot of shield and health and they also have a power that reduces damage taken. For this guy, I used mid- to close-range weapons such as shotguns and assault rifles. The Tech armor is permanent as long as you don't use the O-Sh*t button of making it explode, but even then, the recharge isn't that long. So I would say pull out a heavy hitting shotgun such as the M-11 Wraith or the M-22 Eviscerator. I would then combine that with a light assault rifle, so you are not bogged down by two extra heavy weapons, such as the Phaeston or Avenger, as well as adding an Ultralight mod in there somewhere. For beginners, I would suggest the M-23 Katana and the M-8 Avenger.
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