The first model to come out was a pistol phaser with a small removeable hand phaser attached to the top. This basic model was used and copied till well into the 24th century. The type I phaser, although lacking the higher settings, versitility, and power supply of the phaser pistol, was useful in its own right when a small, easily concealed weapon was needed on landing parties. They were also quite useful on first contact and infiltration missions into a society where technology wasn't as high in order to hide the fact that the away team was carrying a weapon at all.
The Type II phaser became the benchmark against which all subsequent personal phasers were based. Although relatively low powered by today's standards, the Type II was a very versitile tool in it's own day, allowing landing parties to carry a weapon, a welding tool, and a light heating tool all in one. Most importantly, though, the phaser allowed for something which the earlier laser weapons had not, the stun setting. Because of the nature of the energetic particle beam of the phaser, Starfleet personnel were for the first time able to set their weapons low enough just to knock a target out for short periods of time without any permenant damage.
Another advantage that the phaser had over the laser was it's disentegrate setting. This allowed the phaser to be used as a device to clear debris without leaving much behind, unlike a laser which could, at the very least, vaporize a target by melting it, sometimes releasing harmful vapors into the atmosphere.