Most home audio equipment will "work" together, as there is a standardized system of interconnect cables in place today. Speakers can blow if the output of the amplifier is greater than the capacity of the speakers.
100 watts into a 50 watt speaker = Dead speaker.
You may need some rca cables to connect components to each other, depending on what you have on hand, and an adapter cable depending on the type of sound output on your pc.
The general framework of an audio system is Source (cd player, computer, am/fm receiver)-----> Pre-amp/ Amplifier-----> Speakers. Each component is connected to the next by some type of cable. Source to amp/pre-amp is almost always RCA type plugs which are color coded red and white. The connection from the amplifier to speakers is a braided insulated copper wire (speaker wire) of various gage connected to binding posts also capable of accepting banana plugs.
Many systems take a lot of guess work and complexity out of the system by having powered speakers with their own included interconnect. This is 2 speakers with a built in amp in each, connected by a wire. Plug in the speakers, connect a source and you have sound. They are also usually balanced pretty well to prevent damage to the speakers from overloading them.
- Receiver usually refers to an AM/FM receiver which also includes a selector for other source equipment. Most also have an amplifier, but it is important to make sure that the one you choose does or does not, depending on application.
An amplifier is simply that. It may have a gain control on it, or may require a pre-amp (which are also often receivers/selectors). If your receiver has an amp built in, you don't need one, nor do you need one if the speakers have one built in.
I would not use the amplifier you selected for anything. It has a very low output level before distortion occurs, and the MAX output is a dubious rating, which would likely cause the damage mentioned in the previous post, along with sounding "cranked" (noisy, distorted).
These- http://www.amazon.com/...5662&sr=1-1 are only 30 watts total, which would most likely be underpowered for what you described.
These- http://www.amazon.com/Cambridge-Audio-S30-Speakers-Speaker/dp/B00198LYMU/ref=sr_1_1?s=home-garden&ie=UTF8&qid=1314195781&sr=1-1 look pretty good, but will also require the aforementioned amplification.
These- http://www.amazon.com/M-Audio-Studiophile-Powered-Speakers-Previous/dp/B000MUXJCO/ref=sr_1_2?ie=UTF8&qid=1314195953&sr=8-2 also seem under powered, and may not be too easy on the ears. My bet is that they lack range and response.
You definitely want to give stuff a listen before buying it.
The system that Testy posted looks pretty solid, and I know from previous experience that Klipsch makes some pretty good equipment.