Choosing a beginner instrument can be tricky, since the chances are you don't know a whole lot about guitars to begin with. Your first decision involves choosing to learn on an electric guitar, acoustic guitar or on bass guitar. Once that choice has been made, you're going to need to decide on a budget for your purchase. Avoid buying an ultra-cheap instrument - it will not only make learning guitar more difficult, but will have little re-sale value.
These instruments provide the most hassle free way to learn - there's no fussing with amplifiers and cords - something necessary with electric guitars. The drawback is that acoustic guitars are harder to play. A low quality acoustic guitar can make it virtually impossible for a beginner to progress quickly. Avoid cheap pawn shop acoustics - a slightly more expensive guitar will pay off in the long run.
Choosing to begin learning guitar on an electric probably means your budget will have to be slightly higher, to accommodate buying an amplifier. The advantage of choosing an electric guitar is that they are generally easier to play, so you'll notice improvement more quickly. If the music you like tends to be more electric guitar oriented, you'll probably want to start by playing an electric guitar.
Although not traditionally a beginner's choice, the bass guitar can be a rewarding instrument to start learning music on. Because rock and roll bass is generally somewhat easy to learn, beginner bassists will often be playing songs within a few weeks. The downside is that bass guitar often sounds "empty" when not accompanied by a guitar or other instrument.