The beginner (or in many cases the parents of a young beginner) has a bewildering array of different guitars to choose from. Electric, acoustic, nylon-string, steel-string, different shapes, even a variety of colours. Luckily they can be divided into a few main groups, each with pros and cons. These pros and cons need to be taken into account to decide which is the right instrument to start with.

The Inspiration Factor
This is a consideration many people do not take into account, this is why I have placed it first in this article - in an attempt to make people aware of the importance of the inspiration that the right instrument will engender. First, a story to illustrate my point and make my ramblings a bit clearer:

My parents have always been supportive of my musical aspirations. When I came home from school at the age of 15 and announced I was going to be a famous rock guitarist, my mother didn't bat an eyelid. She took me to the neighborhood music store and, on the advice of the salesman, bought me a good quality nylon-string classic guitar and signed me up for classic guitar lessons. I stuck it out for four lessons before giving up in frustration. The problem, I found, was that the sound of this instrument and the techniques I was being taught bore absolutely no relation to the music I was inspired by. A year later I got a part time job after school and after a few months bought my first electric guitar (a Fender Stratocaster - for those with an interest). I have never looked back. An interesting coda to the story is that through my love of rock guitar, I ended up with an interest in (and learning) classic and flamenco guitar too.

So, be careful in your choice of type of guitar. A nylon-string guitar can be offputting to a beginner who has an interest in rock playing. Conversely, an electric guitar is not neccessarily a wise purchase for someone who is fired by the works of Bach, et al. Now on to the types of guitar and the pros and cons of each.

Guitar Types
There are three main types of guitar, which can be identified by the types of string they use. While the notes and layout are the same on almost every guitar, and thus the same piece of music can be played on each, each has a charactaristic sound and playability.

The Nylon-string Guitar
Nylon strings are soft, relatively low tension strings which are easy to fret (push down to the fretboard). This is offset by the fact that the neck of these instruments are wide and thick, making it essential that a beginner learn good technigue - which is good in one respect, but bad for the styles of music which require unusual technique (like blues). The string spacing is wider which allows for involved right hand fingerstyle technique, but is harder to span for the smaller hand. Beginner's classic guitars are also usually available in smaller sizes for the smaller player, but these instruments are usually cheap and nasty and will be outgrown quickly - meaning you will end up buying a few guitars in a short space of time. A full-size instrument is playable by all but the smallest players.
Sound: mellow
Pros: Relatively cheap, soft strings, wider string spacing, smaller bodied
Cons: Wide & thick necks, wider string spacing

The Steel-string Acoustic Guitar
The sound of steel-stringed guitars is louder and much brighter. They are typically larger instruments than nylon-strings, but the neck size is a lot smaller and string spacing is narrower. The strings are metal and very difficult to fret for the beginner.
Sound: bright
Pros: Thin neck, louder
Cons: Hard strings, larger bodied, prices start at a higher range.

The Electric Guitar
The strings are metal, but a lot thinner and at lower tension than steel-string guitars, making them easier to fret. The necks are narrow and thin, making them easier to play for even the smallest player. The bodies are small and thin, but the instrument is relatively heavy. They require amplification and can be loud, depending on settings.
Sound: Can be mellow, bright or anywhere in between
Pros: Soft strings, narrow & thin neck, small bodied
Cons: Can be relatively expensive, require amplification