How to choose speakers for a PC
Monitor speakers or external speakers
While speakers built into a monitor may be a functional option, we are looking for an audio experience far better than that. Audio sources on the computer from music, movies, games, video, and even Voice over Internet Protocol are everyday activities. Quality audio is a joy. External computer speakers deliver this rich experience.
Analog or digital connections
Computer speakers with analog connections that use the common RCA jacks connected to the computer's RCA jacks are just fine. If you're an audio purist or an audio professional you can consider a digital speaker system which has an optical or sometimes a coaxial jack, called S/PDIF, and connect it to the same kind of S/PDIF jack on the computer. Note only some computers have this S/PDIF jack. This S/PDIF connection is considered to deliver cleaner sound because no 'noise' is added to the audio stream from the computer itself. This is because no conversion from digital to analog is taking place inside the PC, that takes places inside the digital speaker system instead.
Integrated audio or separate sound card
Integrated motherboard HD audio chipsets today are high quality and no separate audio adapter card is required.
Recommendations on 2, 2.1, 5.1, 7.1 speaker systems
Ultimately the sound depends on the quality of your speakers. Since computers today are entertainment systems get a good pair of stereo speakers with a separate subwoofer as an indulgence. These are typically known as 2.1 speakers, where the 2 are the number of satellite speakers and the 1 is the subwoofer. You don't really need 5.1 or 7.1 surround speakers.
Recommendations on watts
I recommend 40 watts (RMS) or higher for the total 2.1 speaker system. For example 10 watts (RMS) for each satellite and 20 watts (RMS) for the subwoofer. This will cost around $100. Remember this is for entertainment speakers, for music, movies, gaming and rich sounding video. If you mostly need your speakers for news browsing or other office stuff, you don't need this. In that case just buy a stereo pair with no subwoofer for under $25.00.