Because speech requires a relatively low bandwidth, just about any medium-high quality 16 bit sound card will get the job done. You must have sound enabled in your kernel, and you must have correct drivers installed. For more information on sound cards, please see "The Linux Sound HOWTO" available at: http://www.LinuxDoc.org/. Sound card quality often starts a heated discussion about their impact on accuracy and noise.
Sound cards with the 'cleanest' A/D (analog to digital) conversions are recommended, but most often the clarity of the digital sample is more dependent on the microphone quality and even more dependent on the environmental noise. Electrical "noise" from monitors, pci slots, hard-drives, etc. are usually nothing compared to audible noise from the computer fans, squeaking chairs, or heavy breathing.
Some ASR software packages may require a specific sound card. It's usually a good idea to stay away from specific hardware requirements, because it limits many of your possible future options and decisions. You'll have to weigh the benefits and costs if you are considering packages that require specific hardware to function properly.
Hand held microphones are also not the best choice as they can be cumbersome to pick up all the time. While they do limit the amount of ambient noise, they are most useful in applications that require changing speakers often, or when speaking to the recognizer isn't done frequently (when wearing a headset isn't an option).
The best choice, and by far the most common is the headset style. It allows the ambient noise to be minimized, while allowing you to have the microphone at the tip of your tongue all the time. Headsets are available without earphones and with earphones (mono or stereo). I recommend the stereo headphones, but it's just a matter of personal taste.
A quick note about levels: Don't forget to turn up your microphone volume. This can be done with a program such as XMixer or OSS Mixer and care should be used to avoid feedback noise. If the ASR software includes auto-adjustment programs, use them instead, as they are optimized for their particular recognition system.
As with just about any cpu intensive software, the faster the better. Also, the more memory the better. It's possible to do some SR with 100MHz and 16M RAM, but for fast processing (large dictionaries, complex recognition schemes, or high sample rates), you should shoot for a minimum of a 400MHz and 128M RAM. Because of the processing required, most software packages list their minimum requirements.
Using a cluster (Beowulf or otherwise) to perform massive recognition efforts hasn't yet been undertaken. If you know of any project underway, or in development please send me a note! firstname.lastname@example.org