OK, Here we go. Yo Telepaul! See what I've been saying about the blind man and the elephant? The question I heard you ask is, "What are the different kinds of PA's, and where should I start for a small classic rock band? And- what is this active and passive thing, anyway? And BTW, I'd like to run a bass through it."
Every PA is a combination of a mixer (which is a bunch of preamps with controls that sends however many inputs you have to a smaller number of line outs. It usually has EQ on each channel, and adjustable reverb for each channel), a power amp (which raises the line level to something that can drive a speaker), and one or more speakers (usually in at least 2 identical arrays). Each speaker array is likely to contain dedicated speakers for lower frequencies (woofers), higher frequencies (tweeters/horns), and midrange frequencies (drivers). In larger systems, a single subwoofer is added to handle really low frequencies.
The differences are in quality/price (like everything else in the world), power, number of channels, and what boxes the components are in. A component system keeps it all separate. You use an unpowered mixer (most basic mixers are unpowered), to one or more separate power amps, to passive speakers (ones that don't have a built in power amp).
Another version is an unpowered mixer to powered speakers, such as Eons. This is very portable and simple. The downside is you can't use those power amps to drive anything but those powered speakers. The upside is it's simple, and usually, the amps are well matched to the speakers, because they were built to work together.
The third version uses a PA head or powered mixer to drive unpowered (passive) speakers, It's the same deal, but the power amp is built into the mixer instead of into the speakers.
No matter which version you use, the mixer, the power amp, and the speakers have to match in impedence and in power output/input.
So which is better? No simple answer, dude. It depends on your preferences and your needs. One thing to remember- The more components you have in one box, the more convenient and portable it is, the less versatile and flexible it is, and the more stuff that's out of action if one part of it breaks.
How much power do you need? That also is a matter of opinion. Some real crude guidelines:
100-200 watts, 4 channels- OK for 1 or 2 acoustic folkies in a coffee house
250-500 watts, 8 channels- good for small garage band, small gigs
800-1200 watts 16+ channels- What your average semipro working band uses while they dream of *more power*.
4000+ watts, 64+ channels- You are playing lead on for a headliner
10,000+ watts, 128 channels- Earth, Wind, and Fire (with the horn section and the doo-wops)
100,000+ watts- Woodstock. You can hear it clearly a mile away.
If you want to run bass through a PA, it would be good to have a dedicated subwoofer (usually just one), and a lot more power than you would otherwise need. You can do a small gig with a 50 watt guitar amp. The bass guy probably has 400 watts. You can overdrive guitar amps. Most bass players only want to use a fraction of their available power.
Why all this power? The closer you get to using all your available power, especially with low quality components, the more noise and distortion you get compared to the signal itself. Most folks want a guitar amp to distort on purpose. When a PA distorts, that is a *very* bad thing. Hope this helps.-Richie