Should I record at a higher sampling rate/bit depth, even though the final master will eventually be reduced to 44.1 kHz?
Yes.  While this is one of the most commonly debated issues in the audio field, there are certain facts that can’t be argued with.  First some quick theory:  In analog recording, sound is captured as a continuous waveform, a physical (magnetic particles on tape) “analog” of the sound wave.  In digital recording, we must convert the analog signal into tiny digital samples, which are then reconstructed by the computer to create a digital version of the captured sound.  The sampling rate is the number of times per second that these samples are taken.  In order to accurately reconstruct the signal digitally, the highest frequency present in the sounds being sampled must be less than half of the sampling rate.  Nyquist’s theorem shows that a bandlimited analog signal that has been sampled can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2B samples per second, where B is the highest frequency of the original signal. The converter must therefore filter out higher frequencies in order to prevent artifacts and errors.  Because we only hear frequencies up to 20 kHz, 44.1 kHz was chosen as the standard for a digital consumer audio format, and for listening purposes it is considered acceptable to chop off everything above this.
However, there is a tremendous amount of musical information that exists above 20kHz.  These frequencies interact with each other and combine to form lower sub-harmonics that ARE within our hearing range.  This information is vital to the subtlety and detail of the sound, and is the basic scientific reason behind the belief that analog recording sounds better – in theory, analog recording represents a nearly infinite sampling rate.
So for example by recording at 88.2kHz, you are still capturing sonic information above 40kHz, resulting in a more accurate recording.  The sampling rate should be kept at such high-resolution until the project reaches the mastering stage.  At this point, the mastering engineer will (hopefully) use very high quality converters, to convert the final master down to CD quality 44.1 kHz.
Most any converter worth it’s salt will capture sound at these higher sample rates. The accuracy of this timing and the components within the analog stages of the converter create dictate the quality of the capture.