Zach, if you're on a tight budget, I think you can probably get by with basic fins/mask/snorkel packages you find in sporting goods stores. Body Glove, for example, has several packages of this type, one of which I bought for my wife and son when they got into snorkeling a few years ago.
If you really get into it and you want to make more of an investment, you can upgrade each piece of equipment. For snorkeling or freediving (making descents while holding your breath), I use long freediving fins (these are about three feet long each). These are really great, but they aren't cheap either -- above $100 per pair.
As far as masks go, the most important thing is getting a good fit to your face. The only way to tell this is to go into a store and try on a bunch of masks. I have deep-set eyes and had a hard time finding a mask for scuba or freediving that didn't leak. I ended up with what's called a "low-volume" mask (very little air space between your face and the glass).
I'd put the snorkel as the least critical piece in this equation. For general snorkeling/freediving I use a simple "J-tube" design. If I'm in choppy water I sometimes use a dry-type snorkel (this has a valve at the bottom that's supposed to get rid of water).
I also wear a wetsuit, hood, gloves and weightbelt (which allows me to submerge holding my breath), but these aren't necessary for basic snorkeling. Overall, a simple mask/fins/snorkel package ought to be fine (and much less expensive than buying individual components).
I don't think I quite agree with the comment that snorkeling limits you to tropical shore diving. I live in Southern California and, during the past year or two, have snorkeled or freedived many times from charter boats at several of the local Channel Islands including a neat sea lion rookery, Hawaii, a spring in Florida, cenotes in Mexico, etc. Once or twice I've been on dive boats that have ended up at sites a little outside my depth range, but there's a lot you can see in the water without having to wear breathing apparatus.
As far as technique goes, basic snorkeling is really pretty simple. The main thing is spending a lot of time in the water to build up your comfort level. As far as kicks go, at the outset I'd just suggest keeping your fins under the surface so that you're not splashing around a lot as you move. If you dive down while holding your breath, make sure you equalize your ears (pinch your nose and inflate gently) because you can damage them even just diving down to 10 or 15 feet.
What part of the world are you looking at snorkeling in?
