Jeff,
Getting a live project started, and putting together a "decent" PA system can be tricky. Justin had tons of great advice in his reply, and I agree with everything he said, but can offer a few addendums:
First off, regarding mics: This is a no-brainer, but it bears mentioning: Don't use condenser mics for live applications except (maybe) as overheads on a drum-kit. Big bands with sound-engineers can get away with it. Small bands, in my experience, shouldn't waste their time. Condensers are great for in-studio use, but if you run them through a live PA, you're just asking for feedback city. Dynamic mics generally can't capture the nuances that condensers can, but their small pickup patterns are perfect for controlling feedback in live-PA situations. And truthfully, most live situations aren't ideal for sound-reproduction anyway. Most bands run small or underpowered PA's, don't know how to really use 'em, and most venues have horrible acoustics. Taking all those factors into consideration, it's best to stick with dynamic mics for their feedback-controlling properties.
Personally, I've used the SM-57 as a live vocal mic for years. It took me years to figure out how to get a good sound out of it. Basically, the secret is to apply whatever bass-cut your soundboard has (mine has an 18db cut at 75hz), then take the bass knob of your paramentric EQ and turn it all the way down, as far as it'll go. Just dial all the bass out of the vocal-track entirely. My LOW EQ knob is fixed at 80hz. So, I apply a -18db cut at 75hz, and another -15db cut at 80hz. Just kill all that crap in the low-end. The human voice has no musical qualities in this frequency-range, so you're basically just killing the noise. Killing the low-end will help the vocals cut through the mix better, in part because it keeps your PA speakers from wasting energy trying to reproduce the (non-musical) low-frequency content of your vocal tracks. Once you've killed the low-end, run the vocals as hot as you can get 'em without causing feedback. I don't even worry about overdriving the board, unless it just sounds bad, or unless I start hearing feedback. In many cases, overdriven vocals can sound really cool. The Strokes and the Yeah Yeah Yeahs dig it.
But the Sure SM-57 isn't perfect, and there are certainly better vocal mic's out there if you're willing to spend more money. Sennheiser makes a killer stage-vocal dynamic mic; Paul Karleskint used one for a short while in 351 Windsor. It really helped the vocals to cut-through the mix. Unfortunately, I can't remember its model-number.
Justin mentioned the SM-58. I've got one, and I think it's crap. I never use it. It has a dull, muffled sound. It's supposed to be for vocals, but the one thing you
don't want on vocals is a "dull, muffled" quality. I hate my SM-58, and have never found a use for it. On the other hand, Sure makes a "Beta 58" that's actually pretty darn good. I'm almost positive I used Matt Mayo's Beta 58 to record the vocals for Poseidon's Daughter. Keep in mind, Sure's "Beta" series is actually supposed to be better than their "SM" series, although the word "Beta" might suggest otherwise.
Sure also has a PG series. I think that stands for "Performance Gear." It's supposed to be their budget line of microphones. I've never heard one, but I'd avoid 'em. With microphones, you generally get what you pay for. Cheap dynamic microphones often have a very wide pickup pattern, and will cause feedback problems similar to what condensers will cause. On the other hand, cheap dynamic microphones often make decent room-mics for studio-scratchpad purposes, simply because they pick up everything, and they're not as expensive as a nice condenser.
Regarding the mixer: Mixers are getting cheaper and cheaper, and the quality of today's "affordable" mixers is frankly mind-blowing. I certainly wouldn't recommend getting the Behringer Buy-Of-The-Week if you were a pro looking to run sound for a reputable act -- but as a musician just looking to do a few gigs to get your feet wet, well, you really can't go wrong with any of Behringer's offerings. I can't recommend other bargain brands because I haven't tried 'em. I hear Alesis makes some fine mixers which even incorporate firewire support (which comes in handy if you want to record a show or rehearsal straight off the board). But my $125 Behringer Eurorack UB1204-Pro is a great little device. I've used it in almost every conceivable way you'd use a mixer. I run all my mics and instruments through it in my home-studio to help limit my dynamics and avoid digital clipping. I've used it for my main mixer during live shows. I've recorded band-rehearsals through it. I love the thing, and although I'm sure its preamps don't stand up to Mackie or Allen & Heath preamps, I have to concede that my studio conditions wouldn't allow me to get full mileage out of great preamps anyway. So, where the mixer's concerned: Figure out what you're gonna use it for, and how many inputs and outputs you'll need. Then shop around, and don't be afraid to buy cheap, because the cheap gear can be astoundingly good.
Regarding the power-amp, mains, and monitors: This is the heart of your sound-reproduction system. This is where you will spend the money. Amps aren't cheap, and good speakers will cost you an arm and a leg. My advice: Spend the money on the amp. Get something that provides way more power than you plan on using. I recommend Crown power-amps, because they have a great reputation, and I've used 'em time and time again with no problems.
Do you need monitors? Ideally, yes. As Justin pointed out, vocalists always perform better when they can hear themselves. The same goes for the rest of the band. But every Idiot Plot gig was performed without monitors, including our CD-Release. We got so used to it, actually hearing ourselves play probably would have thrown us off our game. So, yes, you can get along without monitors. In small venues, you will hear yourself well enough from the mains that you won't really need another speaker pointed back at you. But it always helps, and if you've got the money, spend it. You can always unload the equipment on Ebay later.
What about the mains? These are as important as your power-amp. The fact of the matter is, if you buy mains that are perfectly matched to your power amp, they'll last longer and sound better. This means that their power capacity should match your amp's power output, at the same level of Ohms. I forget how this works. When I put Idiot Plot's PA together, I spent a lot of time trying to match affordable components together to achieve the best possible sound at the lowest possible price. Our amp is matched to our speakers, so it supplies ample power, and yet cannot overdrive our speakers. It seems that the homework I did at the time has paid off, because we haven't blown a component yet. I remember back in the 351 Windsor days, when Paul would scrounge-up whatever amp/speakers/board combo he could find for our band rehearsals, and we'd blow the horns out of our speakers on a weekly basis. For a long time, I thought that was just the nature of PA speakers. It was only later I learned that this is the primary symptom of underpowering your speakers. Of course, it can also happen if you're overpowering your speakers to the point of distortion, or if you're having a lot of problems with feedback. Feedback, pops and excessive distortion can blow horns.
So, that's the gist of it: In an ideal world, you'd buy a super-powerful amp, and a combination of Mains and Monitors that can consume exactly the amount of power the amp can provide. If you match your speakers and your amp in this manner, you'll get the most out of your equipment.
But in the real world, most of us can't afford to buy a super-powerful amp
and the great speakers to match. Most of us want to buy small, and upgrade later. Since it's always better to overpower your speakers than to underpower them, the wise move is to buy a killer amp, and so-so speakers. Don't worry if you're not consuming all the power your amp can provide; this isn't efficient, but it shouldn't damage your equipment like having an underpowered amp will. And when you start making some dough at your gigs, then you can buy the better speakers and have a great PA system.
That's all I have to say on the matter.
You may find a ton of help here:
studio-central.com/phpbb/index.php-- Ryan