Ok, there is a lot of info on the web about this stuff but most of it is very technical so I'm going to try and break it down for you as simple as I can. Here goes:
Speakers and amps are all rated by their
impedance (meaning resistance which is measured in
ohms) and power output or watts. The most important thing to remember is that you match the amps and speakers ohms and watts ratings to avoid damage to either.
ohms - The higher the ohms (resistance) the more power is required from the amp. Most consumer DJ speakers are rated at 8 ohms and sometimes 4 ohms. Higher pro power gear can go down to as little as 2 ohms, but that's mostly huge setups like for clubs or concerts. Whatever the wattage or power rating of your speakers, be sure that the amp you use is rated at the same ohms - 8 ohms speakers with an amp rated at 8 ohms; 4 ohms speakers with 4 ohm amp, etc. If let's say you use speakers rated at 4 ohms and your amp is only rated for 8 ohms, then the amp will need to put out twice the power its rated at resulting in overheating, clipping (amp shuttng itself down to prevent damage) and burning out the amp. Some amps are rated to be used at different ohms. Some even have switches to change to the ohm rating you need. Check the specs on the amp to see what ohm loads it handles. Here is a typical amp spec:
300 watts per side @ 8 ohms (the ohms is rating of the speakers being used)
450 watts per side @ 4 ohms
600 watts per side @ 2 ohms
1200 watts bridged mono @ 4 ohms (Bridging is when both channels are linked to work as one mono channel)
As you can see, the lower the ohm ratng of the speakers, the higher the output or more wattage the amp can put out.
Speakers - the speakers will be rated by ohms (covered above) and by watts. The watts are usually rated as watts RMS (Root Means Square) or this is sometimes referred to as continuous power. Basically this is the watts that the speaker can safely push for an extended period of time without damage. You will sometimes see them rated with their peak watts also, but while this is important, it is a bit deceiving because this is the wattage the speaker can only put out for very short bursts of time. The speakers can't be run at the peak wattage rating for long periods or you'll blow them out. So be sure you go by the RMS or continuous watts rating versus the Peak watts rating.
If you're just starting out and you really don't need a huge powerful setup, I would suggest going with speakers and amp rated at 8 ohms, and be sure that the amp is powerful enoug to push the wattage the speakers are rated at. If the speakers are 8 ohms and push 250 watts RMS each, then the amp should be 8 ohms and push at least 250 to 350 watts per channel, but not much more or you'll blow the speakers. Never use an amp that isn't powerful enough to push the speakers because it will blow out and could damage your speakers too.
It's good to arm yourself with some knowledge when you go shopping for your gear, but I would follow misscc803's advice and go to a shop where you can test out and listen to the gear and hear the difference between a 250 watt speaker and a 1000 watt speaker. Check the forums here and audiogear sites on the web like
www.zzounds.com for gear reviews and suggestions. Good luck!