The guns are "unlocked" as you find them scattered through out the game. Level 1, 2, and 3 have 1, 2, and 3 weapons to pick up respectively. Other levels have about 4 or 5. After you find a gun and finish the chapter, you can then choose it as your starting primary weapon in the challenge levels.

Ripper
Primary: Hold the trigger down to hold a spinning saw blade out in front of you. Move it around to cut limbs off and block enemies from grabbing you. Though each blade lasts long enough to cut through multiple enemies,but it is very short range only letting the longer range physical attacks get you. It does however push them back or cut limbs off, though only to one necromorph at a time.
Secondary: It shoots one of the blades straight out with a good rate of fire. It is similar to the horizontal plasma cutter, but a good hit will take down an enemy instead of just a limb and it will go through multiple targets. Make this your primary use and stasis enemies to get that good head/neck shot.

Line Gun
Primary: It shoots a very wide beam that travels through enemies and deals massive damage, but they travel noticeably slow enough that moving enemies that are far away are difficult to hit. A decent upper body shot will sever the head and arms of most targets.
Secondary: Fires a mine that has a huge explosion, though it has a delayed timer. Those just outside of the kill radius will be knocked down.

P-Sec Pistol
Primary: High rate of single shot fire, though pretty low damage.
Secondary: Knocks back enemies more so then primary, trading off lower rate of fire, extra ammo usage, and less damage. Stick with firing primary real fast.

Pulse Rifle
Primary: Very high rate of fire and holds enemies from advancing. To conserve ammo try shooting in quick bursts.
Secondary: More like a shotgun blast with a wide dispersal. It takes more time then I'd like to charge. Haven't found a use for it yet.

Flame Thrower
Primary: Great at crown control, primary actually has a short to medium range. It sets them ablaze and halts them in their tracks even knocking them back some. I find that repeatedly firing works better then holding down the trigger to spray them knocks them back a little more and conserves ammo since your not firing at the nothing between the targets. Then quickly switch to the rivet gun to add a shot or two.
Secondary: Missing your target may still cause some damage from a small explosion, but not much considering it uses up extra ammo. There are better guns for medium to long range.

Arc Welding Gun
Primary: Even fully upgraded, it doesn't arc all that far so the enemy needs to be packed pretty tight. It does decent damage, though chews through ammo. It does however have a good knock back, so instead of holding down the trigger for those close up or medium range targets, fire repeatedly at them.
Secondary: Fires an almost instant travel ball of energy that lashes out at necromorphs and has a small knockdown explosion, however it uses up 5 ammo per shot so even secondary uses a lot of ammo.

Contact Beam
Primary: Difficult to use as it needs to be charged (i.e. incredibly slow fire rate), but it is very powerful. The shot is instant travel, does massive damage, and has an explosion damaging and/or knocking nearby necromorphs down.
Secondary: Area knock back is very strong, but is only short range.

Plasma Cutter
Primary: Great general use weapon. Decent damage and with a little width and instant travel time that is good for targeting limbs.
Secondary: Honestly, I just use primary.

Force Gun
Primary: Good crowd control that hits all nearby enemies, knocks them back, and does damage. If you are surrounded, this is very good.
Secondary: Shoots a bouncy grenade (doesn't bounce much, though I wasn't shooting them very high or off walls) that explodes when it contacts an enemy or after a few seconds. It is basically a primary shot, but originates from the grenade and is good for grouped enemies, however it is less damaging then primary.

Rivet Gun
Primary: Your unlimited ammo gun.
Secondary: Good for lone enemies that you can take your time with or getting in a few very long range shots at legs.