Heat/energy weapons are good for shields and kinetic weapons are good for hulls. So yes: lasers take down shields and canons and missiles damage hulls.
There three types of offensive weapons:
Fixed (F)
Gimbaled (G)
Turrets (T)
There are also defensive mines that you drop behind you, in your attacker's way.
Fixed weapons are the most powerful but you have to target with your entire ship, old school, so you need to keep your target in your crosshair all the time. Fixed weapons are best on agile ships like Eagle and Vulture.
Gimbaled weapons are mounted on gimbal mounts so they can move around some and track your target, but you still need to be facing in the general direction of your target. Gimbaled weapons do less damage and cost more than fixed weapons. These weapons are jacks of all trades for general use ships.
Turrets are self-firing self-targeting weapons. They're the weakest and the most expensive. These are good for slow ships and they do have limits. They're limited by the shape of your hull and your hard point placements because they need to have line of sight (LOS) to the target. They also have couple of modes of firing which you adjust in the System Panels on the right side.
So a given weapon may come in three versions. For example there are fixed, gimbaled and turreted beam lasers. You pick the the right type based on your ship type, maneuverability and flying style.
Read the Wiki about ships.
http://elite-dangerous.wikia.com/wiki/Ships
One of the most important characteristics for combat is maneuverability (agility) and it's shown on a scale from 1 to 10. 1 is the least agile (such as a slow, big cargo ship) and 10 is the most agile (such as a small fighter). Eagle (10) and Vulture (9) are the most agile and they do best with fixed weapons as they're the most powerful type of weapon. Ships with low rating like below 6 will not able to use fixed weapons agains most attackers as the attackers will easily outmaneuver them and get out of their LOS.
I tried both Vipers and I felt like Cobra Mk III was a better choice because it is rated at 6 in terms of agility AND can carry class 4 shields and has the same hard points. It's also the fastest ship so if things go wrong you can boost away and jump.