I'm looking at the PreSonus Audiobox 22VSL USB 2.0 and it says it has the option of 44.1kHz, 48kHz, 88.2kHz, and 96kHz sample rates, but it says its digital to analoge and analoge to digital conversion dynamic range sample rates are "114dB, 48kHz sample rate, A-wtd" I was wondering which sample rate should I be paying attention to and what the difference between the two are.
"48kHz sample rate, A-wtd" is just telling you under what conditions the "114dB" dynamic range reading was achieved. It doesn't really tell you a-lot in all honesty, however almost all modern audio interfaces (including this one) will be more than cable of a decent quality recording and sound reproduction.
In regards to sample rates it's not something to get to hung-up about, many arguments come about related to sample rates, but in reality 44.1kHz is 'more' than adequate for any regular audio needs, 48kHz is very handy for the purpose of audio for video for compatibility reasons.
To justify my reasoning behind this, first read up on the Nyquist-shannon theorem. This states that a signal can be perfectly reconstructed provided that the maximum frequency (bandlimit) does not exceed half of the sampling rate (i.e. recording at a higher sample rate does not provide more information as the signal can already be 'perfectly' reconstructed, it is not an approximation!). So given this information a sample rate of 44.1kHz allows a theoretical maximum frequency of 22.05kHz before an effect known as 'aliasing' occurs. One argument is that this would require a very steep low-pass filter to prevent any frequencies exceeding 22.05kHz getting through (and causing aliasing), while allowing all frequencies below 22.05kHz through. However consider that at very best our ears can hear a maximum of about 20kHz, this would have to be quite a high level in comparison to other frequencies as we dont hear all frequencies of equal level (Equal Loudness Contour), and to be honest you will soon find anything above about 17/18kHz isn't really desirable (you may not even be able to hear it!).
If your end medium is going to be a set sample rate (such as CD at 44.1kHz or video at 48kHz), then it may be worth sticking to these rates which reduces possibility of other noises being introduced at the conversion stage (see: src.infinitewave.ca). I'll add one more point and that's, if you need to capture frequencies outside the audible range or would like to for whatever purpose then of course 88.2kHz or 96kHz or even higher sampling rates are acceptable choices, but remember that few microphones can capture frequencies this high!
For some further reading on the subject should it interest you try these:
also check out Lavry-engineering if you become interested from a more technical point of view.