These are my thoughts on the humans weapons. Impressively all of them are useful in the right situation so it's just a matter of knowing when to use what. I know other people have other strategies that work well so feel free to share.
Rifle
The Rifle is pretty decent in all situations but is rarely the best choice if you can afford something better. The only thing to remember is that if you're deciding between the Lasgun and the Rifle, the Rifle can actually do more damage in the same amount of time when reloading is not a factor. For brief encounters at short to mid range (like when you need to just pop outside your base to repel an attacker) or when attacking light alien defenses and accuracy is not necessary the Rifle is the better choice.
Painsaw
Though it has the highest damage output of all the human weapons, the Painsaw is not primarily for attacking aliens. With a range less than even that of the Dretch's melee attack you're an easy target for anything not taken by surprise. What the Painsaw excels at is taking down bases in a hurry - if you're at an Armoury and someone says the Overmind is down, take a Painsaw and clean up. It works just as well on your own base if you're moving and don't want to visit the old base undefended or waste time with the deconstruct delay (not recommended for servers that auto-ban for teamkilling). If you're crazy enough you can try forging a path through the alien defenses and taking out the Overmind yourself. Cover from teammates is always recommended.
The one situation where it's appropriate to attack aliens directly with a painsaw is when a large alien (tyrants mostly) assaults your turrets - jump behind the alien to block its exit and saw away. It may kill you in trying to retreat, but it will die if anything else keeps shooting it.
Shotgun
The Shotgun is a short range damage dealer. When every pellet hits you do a whopping 56 damage, more than even the Mass Driver. The big spread makes it best suited for big aliens. The low price makes it a reliable standby for repelling massive alien attacks or even just regular patrolling. One thing to remember is that versus Basilisks and Advanced Grangers the Mass Driver is a better choice - the Shotgun will require at least two hits to kill, the Mass Driver will only take two and works at any range.
Lasgun
The Lasgun is an endurance weapon and early game base killer. Other weapons are available for less and can do more damage but no weapon is as relentless as the accurate, rapid-fire hitscan Lasgun. Its accuracy allows it to chase down fleeing enemies at any range (important against Marauders, and Grangers in endgame egghunts) and take down alien defensive structures from safe vantage points without wasting ammunition. Its lack of reload gives enemies no opportunity to attack safely, forcing them to choose between risking the damage and fleeing outright. For this reason it is an especially good support weapon for stronger weapons with shorter effective ranges (Painsaw, Shotgun, Flamethrower, Lucifer Cannon). Only take a Battery Pack along if you intend to be out long enough to use up more than 200 cells.
Mass Driver
The Mass Driver is a tricky weapon. It requires quite a bit of skill to use and actually does less damage than some cheaper weapons, with the Lasgun in particular being also just as accurate. Its strength then lies is its ability to deal large chunks of damage suddenly at any range. Smart alien players will watch their health during an assault to gauge when they should retreat to safety; with the sudden appearance of a Mass Driver they can be easily pushed past the threshold of comfort. Because of its difficulty and low average damage output, support from rapid fire weapons or defensive structures is always recommended. Taking a Battery Pack is also always recommended if you can afford it as the reduction in reload times can mean the difference between survival and death. If your aim is good enough it is the best weapon for killing everything below Advanced Basilisks (especially dretches early in the game); for higher aliens it should only ever be used as support.
Chaingun
The Chaingun is the best "Fuck Off" weapon. Its large spread makes it a poor choice for initiating fights or attacking alien bases but not so poor as to make chasing down injured aliens difficult. Bigger targets are of course easier to hit and any Tyrant or Dragoon that doesn't have an escape plan after attacking a turret front will be easy credits. Works well as a support weapon for accurate base killing weapons like the Pulse Rifle and Lucifer Cannon. Not at all recommended without a battlesuit (which enjoys a reduced spread without crouching) except when you have a very good reason to sit on a turret in defense.
Pulse Rifle
The Pulse Rifle is a base killer with a defensive punch. Its accuracy, range, and damage output make it suitable for destroying alien structures from safe vantage points (replacing the Lasgun in this regard at Stage 2). Its high firing rate makes it suitable for short range defense but being a projectile weapon hurts its effectiveness at chasing down injured aliens. For these reasons it complements the Chaingun extremely well. Unless you need a Jetpack, a Battery Pack should always be taken with the Pulse Rifle for base raids. Using a Battlesuit is generally only appropriate for defending against Tyrants and Upgraded Dragoons.
Flame Thrower
The Flame Thrower is hot. Its only downsides are its range and its propensity to damage the wielder. The latter can be controlled through discipline and the former just means that aliens can avoid attacking you until you start torching their base. Anything below Dragoon is easy barbecue and even the highest alien classes will have to kill you fast to avoid going down in flames. Smart aliens will dance around you to try to get you to waste your ammo and accidently burn yourself, then attack from behind while you're distracted. The last thing you want is to be goaded into a "Fire Blossom" attack - spinning around spouting fire until you kill yourself.
Lucifer Cannon
When wielding the Lucifer Cannon its important to remember that you're in charge. Unless you want to milk some credits from Dretches beforehand, your goal with a Lucifer Cannon should always be to take down the alien base. Never allow low class aliens to distract you from this as its very easy to waste ammo on aliens not determined to attack you. Only ever attack aliens as a means of defense. If you don't think you can pull off enough fully charged blasts to kill a large alien before it kills you, fire one then try bluffing with the secondary attack. Never make it obvious that you've run out of ammo; always retreat with at least enough to make it clear that you're not empty yet. Since you're highly likely to hurt yourself during normal usage and 600 credits is something of an investment, it's always preferrable to take a Battlesuit over a Battery Pack. The lucifer cannon can work well for killing tyrants but remember that it is still a defensive weapon in this situation; if a tyrant can retreat (which gets progressively harder the more teammates you have wielding longer range weapons) it can't be killed by a lucifer cannon.
EDIT: Rethought the importance of using a Battery Pack with the Pulse Rifle
EDIT 2: Added painsaw defense strategy, mass driver for chasing, chaingun to be used with battlesuits, and lcannon versus big aliens
