The phenomenon of sound is a combination of two components: the fundamental and the overtones. On your guitar, the fundamental is the lowest order of vibration from the moment you strike the string, and the overtones are 'related' notes that develop through fractional division of string vibration and sound waves. The fundamental and the overtones combine to create what your ear perceives as one sound. To a large degree, the 'voice' of an instrument is determined by the fundamental/overtone relationship. This is part of the reason why each guitar has a unique sound.
Have you noticed that the pickups you stick in the soundhole or under the saddle of your acoustic guitar sound dull and one-dimensional? This isn't because they're bad pickups but because they mainly reproduce one part of what your ear is accustomed to: the fundamental. To complete the sonic picture you need another source capturing the overtones. Microphones and 'contact' pickups are both good for this. So good that, in many cases, they reproduce too much of the overtones, creating a sound that is acutely 'live', the opposite effect of the magnetic and under-saddle pickup. Hence the need for two separate pickups, one for the fundamental and one for the overtones. Mixed together they create a composite sound that assimilates what's really happening on your acoustic instrument.
If you agree with the above stated, it's time to think about which pickups (and/or mics) to choose. There are so many models currently available the choice can be overwhelming. It's up to you to decide if you're more fond of the magnetic/soundhole type pickup or under-saddle transducers, and whether you prefer internal microphones or 'contact' pickups. Each has its pros and cons. Consider your playing and performance needs. If you're a flamenco or classical guitarist (using nylon strings) a magnetic pickup isn't going to be very useful. Also, check out the technical specs on each product. Things like output volume, signal-to-noise ratio, and price will go a long way to help you make your decision.
Since the focus of this article is the fundamental/overtone relationship as it applies to amplification, not what brand of pickups to purchase, I will leave the extensive critique of pickups until Zen and the Art of Acoustic Guitar Amplification, part 2. But, I believe that even if you choose the least expensive magnetic pickup and microphone on the market, you'd be closer to achieving a true acoustic sound than if you purchase one of the higher quality pickups that only reproduces part of the equation. There are some pickups that try to integrate both elements into one signal, but I feel these are inadequate. You need to have completely separate equalization and volume control over each pickup because they represent totally different dimensions of the sonic picture.
What happens once the signal leaves your instrument is as important as your choice in pickups. Get the best quality cables you can afford. A good cable will provide clearer sound with less noise. Another consideration is the cable length. Some pickups are active (and low impedance). For these the cable length is less of an issue. For high impedance pickups, though, you'll want the shortest cable before it reaches the preamp. A high impedance signal will loose high-end with each foot of cable length. As a rule for high impedance pickups, try to keep the cable less than ten feet before reaching the preamp.
Next you need to decide on a preamp for each pickup (that's right, each pickup needs its own separate preamp) before you send your signal to the PA. Make sure that the input impedance of the preamp is higher than the pickup you feed into it. Many preamps are simply meant to amplify a weak signal. Others have equalization, notch filter, phase reversal, and effects loop built in. You can also use a self-contained amplifier (similar to an electric amp with preamps built into it), which allows you to generate a substantial amount of on-stage sound. This comes in handy as a personal monitor or if you play with a band and need to compete volume-wise. Good results can be achieved with any of these scenarios.
After all this you will face the ever-present challenge of the gig. Conquering room acoustics with proper equalization is indeed an art which your ear will become more attuned to over time and with experience. But to have a fighting chance I truly believe you need to assemble a high quality, flexible setup that accurately reproduces your guitar's sound and overcomes the environmental circumstances that are part of live playing.
If you are interested in learning more about overtones in music, please consider Henry Cowell's "New Musical Resources" (ISBN 0521499747).