I am building an audio amplifier using a lm386 amplifier with a 12 volt supply driven from a headphone jack. I am looking for a speaker that will work well in this setup. Currently I am using a small speaker and their is a lot of distortion in the sound. I am looking at a speaker that is rated for 1 watt and has a frequency range of 180Hz ~ 10kHz. I was not sure if this would be good enough for a good sound quality when playing music. Please tell me if this would work with my setup. Here is the link to the speaker I am looking at http://www.digikey.com/product-detail/en/GF0771/GF0771-ND/304442
Be careful with the power ratings of speakers. In the hifi community the power rating is not understood as a value where the speaker performs best. It's understood as a value which, if exceeded breaks the speaker or produces very bad sound results. When picking speakers, you usually multiply the power ratings by 3-4, just to be sure.
Before searching for speakers check your amplifiers total output power!
Regarding frequency: 10khz is not enough for a decent music quality. Low quality audio hardware ranges from 50HZ - 16khz.
Decent quality would be 18Hz to 20kHz. Now, a single speaker usually does not perform well over such a wide range. That is why normal speakers are build of a tweeter (for high frequencies) and a woofer (for low frequencies). The woofer plays everything from 50-2khz, for example, the tweeter plays everything else. The signal is split with a high pass, for example.
There is a solution for that problem as well:
Look for a broad band speaker. They are usually ranged from 50Hz - 16kHz. They are not meant to play to loud, though.
One more thing: Keep in mind, that even if a speaker is rated as 180Hz ~ 10kHz it won't perform the same on all these frequencies. Some frequencies will be louder, others are choked. Check the frequency response diagram for the speaker if available.
Try finding PC speakers, somewhere. Maybe even old ones, people dump them everywhere, for no obvious reason. You might know someone who can give you a pair.