This can be an incredibly hard process for someone that doesn't have much knowledge in the area of sound, but there is some information that if you know ahead of time will make it much easier. The first is to know how much you want to spend. PA systems run anywhere from a couple hundred dollars to thousands of dollars - quite the range, so know how much you want to fork over before you walk in the store and see what the state of the art speakers can really do. The second thing is to know how large of an area you want to interact with. If the sound system is supposed to be used in a larger room and not moved then you probably won't need the best sound system because sound fills a room very quickly. However, if you are planning on transporting this sound system around and possibly using it outside then you may want to push for something with a little more power. You want to error on the side of having too much power when buying a sound system if you can help it. And the third thing to know when buying a sound system is what you are going to use it for. If it is just to make public announcements then the mixer isn't really important - maybe a mute button and a fader switch for the adjustment of volume would be fine. However, if you are planning on using this for instrumental or vocal performance you at least need to look into getting one with 3 Equalization channels on the board and probably one with more than two channels to plug in.
Most of the brands of sound systems are alike. Some are a little better, but for the most part you are looking for what you want in the price range that you want. Don't just go for the more expensive because it has the name Bose on it. Most of the brands are great. Some of the quality sound system brands are: Bose, Yamaha, Crown, Mackie, Behringer, JBL, Shure, and Audio-Technica.