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Audiophiles may like 80's retro hugeass speakers, but for regular home use you don't need to spend a lot of money. Micca is a good brand that has some quality speakers for around $80 for a pair.
Logitech make some pretty good speakers too. Logitech Z623 speakers + subwoofer are very good quality-wise, and if you want surround sound, there's Logitech Z-906 which consists of 5 speakers plus subwoofer. Both reasonably affordable.
2.1 is the best way to go when you're listening to music. Music is rarely more than stereo. 2.1 means that there is 1 left speaker, 1 right speaker, and a sub woofer. The left and right options can either be powered, or passive speakers. Passive speakers require an Amplifier to make them work, whereas a powered speaker will plug into a wall socket for power and doesn't require an amp. Good stereo speakers will be passive. But powered 2 channel speakers are still better than the shitty desktop speakers most people use.
5.1 is kind of like 2.1, except there are 5 speakers and a sub woofer. This is also called "Surround Sound". In addition to 2.1's Right, and Left channels, this also adds a "center" channel, and 2 "surrounds". This type of setup is commonly used in home theater setups. Normally the speakers in "surround sound" setups are lower quality, because people don't want to buy 5 expensive speakers and a sub woofer.
7.1 is yet another home theater setup. It adds two speakers to the 5.1 setup. 7.1 splits the surround channels into 2 "surrounds" and 2 "rears".