Maybe the different advantages that different weapons have are something like this:
Laser weapons - standard sidearms across much of Starfleet and very popular among private agencies such as mining colony autorities - they are in many ways very efficient, developed specifically for use in space, where a projectile might puncture critical machinery - destroying through the application of heat energy, forcing apart molecular bonds - but their main drawback is the lack of any kind of stun mechanism, for which reason, Starfleet prefers to equip it's officers with phaser weapons, and eventually wishes to move away from lasers entirely.
Phaser weapons - unparalleled in their destructiveness, capable of vaporizing a target, they are feared throughout the galaxy for their ability to inflict devastating wounds - they operate by forcing a stream of matter/antimatter particles, rather than light photons, at a target - Starfleet has judged particle weapons to be superior to plasma and laser weapons - it incorporates the non-violent stun setting into all it's sidearms, in which the particle stream delivers an electrical shock to the target's nervous system - the higher settings can conduct such heat as to destroy large portions of skeletal tissue with a mere glancing hit, the energy radiating out by diffusion - only the point of contact with the target feels any of the intense heat as the beam confines all energy like a force field.
Plasma weapons - a throwback weapon, technologically speaking, the plasma weapon is still popular throughout the galaxy, and is commonly found among civilians, as well as the planetary forces of many minor governments - the only older type of weapon is the explosive-powered projectile weapon (or slug-thrower), but personnel are never likely to encounter something so archaic in standard operations - the plasma weapon works by directing a bullet of plasma energy against a target, causing severe burns against internal organs.
Ordinance - Starfleet is equipped with photon grenades, which work much like photon torpedo - delivering huge antimatter explosions up to a 0.1 kilotons of TNT - and can also be used with Starfleet's infantry mortar system, for use in battle conditions - it also (rarely) employs the photon missile launcher, a device capable of downing a shuttlecraft - and standard chemical explosives for forcing open doors and breaching fortified - Starfleet is however, an exploration and peacekeeping organization, so these capabilities are rarely deployed.
Alien weapons - Starfleet personnel are likely to encounter the Disruptor Pistol and Disruptor Rifle in their travels - used extensively among the Orion Colonies, Klingon Empire, Breen Confederacy, and Romulan Star Empire, it is the most popular particle weapon technology in the galaxy, thanks to Klingon arms exports, and operates upon similar principles to the phaser, but is designed to cause massive destructive force to the nervous system of humanoids in ways that violate United Earth's 2089 Melbourne Convention treaty on the use of directed energy weapons.
Doctors dread phaser and disruptor wounds - they may have to deal with partially vaporized victims, who were still alive, but may have lost entire portions of their musculature, skeletal structure, or skin.