The guitar is far and away the most popular musical instrument to learn to play. It's prevalent in nearly all kinds of popular music and kids and adults alike to seem to gravitate towards it as their instrument of choice. It's an extremely versatile instrument and in terms of instant gratification, it's probably second only to the piano. By the end of your first day with a guitar, you should be able to play at least one or two popular songs. That being said, the decision on which guitar to purchase first is not one to be taken lightly.
The electric guitar is probably the first guitar of most aspiring musicians, mainly just for the cool factor, but from a practicality standpoint, I believe a novice should select an acoustic first. There are two primary types of acoustic guitars, the steel string variety and the nylon string variety. The nylon string acoustic is used primarily for classical style music and if that's what you want to learn, then the electric guitar is of no use to you. The steel string guitar, however, is a logical first step into the eventual purchase of an electric guitar.
The acoustic is preferable to the electric as a first guitar for several reasons. First, entry level acoustics are typically less expensive than entry level electrics. Since a lot of guitars will just end up collecting dust in a closet after a few uses, especially if purchased for children, this is no insignificant point.
Second, an acoustic guitar often has slightly thicker strings that are spaced further apart. This really helps a budding guitarist strike the strings cleanly and learn the fine motor skills necessary to form the chords. The strings on an acoustic guitar are tuned with greater tension than on an electric guitar. This makes the transition to electric seem easier because less pressure is required to sound the note. This is equivalent to a baseball player swinging a heavier bat in the on-deck circle in order to make his regular bat seem lighter.
Third, acoustic guitars are better suited for private practice time. They're quieter, and far more portable. An electric guitar is meant to be played loud. Making an electric guitar sound good loud is just another unnecessary task for the beginning guitarist. Amplifier selection and tones have to be taken into account, and even professionals spend endless amounts of time tweaking their sound. An acoustic guitar just has to be tuned before you play it.
An acoustic guitar should not be seen as just a transitional instrument however. Even the hardest rockers pick up their acoustic from time to time. It's great to sit around with some friends and sing a song or two or take on a camping trip without the need to lug around an amp or search for a power outlet. Both types of instruments have their strong points, but the acoustic guitar is the ideal first instrument for the aspiring guitarist.