Back in the day a hi-fi was simply a pair of speakers, an amplifier, a turntable, and maybe a radio or tape deck. Nowadays even the speakers are optional, and the rest of the system is an open question.
With "regular" speakers you have to think about getting an amplifier or maybe a receiver, and this is where it can get a little complicated. And what sources are you planning to play through the system: a turntable, CD player, iPod, radio, TV, games, or Internet radio?
You can eliminate the amp/receiver if you buy self-powered speakers (with built-in amps) or maybe all you need is an iPod speaker. If you want the best possible sound for the fewest dollars don't buy speakers at all, get headphones instead. Consider whether you want to buy a complete system right now, or buy something just to get going, and then upgrade parts of the system down the road.
Regarding speaker and amplifier matching, don't worry about the speaker's power-handling specification. I get this question a lot: "Can I use a 200-watt amplifier with a 100-watt speaker?" And my answer is always the same: yes. The speaker power-handling spec is totally useless--it implies that you couldn't possibly harm a "100-watt speaker" with a 50-watt amp, but if you overdrive the amp the speaker will probably break. The opposite combination, a 200-watt amp with a 100-watt speaker, would be less likely to blow up the speaker, because the more powerful amp is less likely to distort when played loud. In short, don't worry about the specs; just be aware that bigger speakers can usually play louder, with less distortion, and make more and better bass than small speakers.
With most receivers, sound quality is a lower priority than piling on features, so I'd recommend buying a stereo-integrated amplifier. The digital-to-analog converter (DAC) can play just as large a role as the amp in determining the sound quality of the system. The same logic applies to turntables: get the best one you can, but speakers (or headphones) will make the biggest difference in sound quality.
What's the "best" speaker? Good question, but there are too many variables of room and speaker size, how loud you like to listen, budget, types of music, subjective sound quality issues, and appearance to come up with a single answer, or even a single answer for each price range. Based on my experiences as a hi-fi salesman for 16 years, preferences differ enough that selecting a "best" speaker in a given price class that would make everyone happy is an impossible task. Of course, my opinions of specific products are covered in my CNET reviews.
With all of those precautions in mind, here are a few recommended "systems," in ascending price order. Let's start with a pair of MonoPrice 8323 headphones ($21) plugged into your computer (substitute better headphones as budget allows). Moving up from there, you could get some Audioengine A2 powered speakers ($199/pair), again for use with your computer, or for double the price, the Emotiva Airmotiv 4 speakers ($399/pair).
For regular speakers I like the Wharfedale Diamond 10.1 ($349/pair), matched with a JoLida JD301RC integrated amplifier ($425), and a Schiit Audio Bifrost DAC ($349) or a Rega Research P1 turntable ($395). If you have a big room, and really want to party, go for bigger speakers, like the Zu Audio Omen Standard ($1,500/pair) with a Peachtree Audio integrated amp/DAC ($1,799).
If you're lucky enough to have a hi-fi store nearby where you can touch and feel and hear some gear, that's the best way to educate your ears. If that's not possible, you can always read my CNET reviews, and buy products you can return if they're not up to your expectations.