A type-1 phaser was the smallest, most basic weapon carried by Starfleet and other Federation personnel. Type-1 Phasers were typically carried when it was inappropriate to carry a larger weapon, such as on diplomatic missions, or "undercover" work.
The Type-1 had eight adjustible settings, ranging from stun to heat through disruption to disintegration. The 23rd century type-1 in use in the 2260's incorporated a small flip-up sight, and was fired by a trigger on the bottom front of the unit. Several versions of the Type-2 Phaser incorporated a Type-1 Phaser into their design.
In 2369, Benjamin Sisko used one of these particular models of phaser in dealing with Bajoran terrorists placing bilitrium grenades in Deep Space 9's docking pylon 3. (DS9 video game: Crossroads of Time)