I am new to Audacity and am using an Art phono preamp to archive my analog recordings. I am using Windows 7. I have an external FireWire drive I use for Pro Tools and an external 2.0 USB drive. Would it be beneficial to use either of these drives to record.
No, it is better to work on the local hard drive. Recording and playback require that the audio data is available as a continuous stream without interruption. USB in particular may have unexpected delays reading or writing that can cause dropouts and other errors in the data, which could even cause the application to freeze or crash. I would guess that a firewire drive would probably be ok, but I don’t have one so I’ve never tested that.
It’s OK to transfer files to external drives when you have finished working on them, but not that for Audacity (and ProTools) the audio data is separate from the project file. See here for how to safely move Audacity projects: http://manual.audacityteam.org/o/man/audacity_projects.html
Note also, that after an Audacity project has been saved, Audacity uses the project “_data” folder for temporary data, not the default “temp” folder. If you wish to resume work on a project that you have copied to an external drive, it is best to either copy the AUP and its associated audio data back to the internal drive before you start work, or, open the project from the external drive and then save the project to an internal hard drive before you start work (so that the project that you are working with is on the local hard drive).
Tip: After moving or copying important projects - check that they still play ok all the way through.
Tip 2: Moving or copying ordinary audio files (such as WAV files) is easier and safer than moving / copying projects, because a WAV file is just one file, not thousands of little bits.
WAV files are straight A->D, piling up PCM data into a HUGE file, and usually stereo (twice the data). Maybe consider FLAC? or is there a good reason for using WAV? that over-rides the size?
To mention an example or two of “thousands of bits”… one day I had recorded 2 hours of stereo audio but didn’t export it, and left Audacity on the desktop. It might have been minimized for a while. Then around 9 pm, decided to do a disk cleanup with CCleaner. Sometime later, decided to save (Export) the audio, but there WAS no audio to save!! 
Another time, did a disk defrag with Audacity OPEN, and could actually see 100’s or 1000’s of sectors lighting-up YELLOW as they were consolidated.
-Ed
If the Audacity show is all mono (centre panned mono tracks), then the exported file is mono, so no doubling of data.
No problem with using FLAC other than some audio programs don’t support it without installing additional codecs/filters. Flac also has the benefit of good metadata support.
Rule #1 of any maintenance, especially defragmenting: close all running programs, restart and don’t use the computer at all during maintenance.
Personally, I steer clear from all these 3rd party cleaners. Most of them are buggy as hell and any half-decent OS shouldn’t need defragmenting at all. As I also offer data recovery as a service, I don’t mind others using them as they are the #1 source of data loss… 
You have very fuzzy computer management. Never leave a show hot while you go to lunch and never do machine maintenance with any programs running.
Win. 7 will cheerfully defrag itself. I think you have to leave it up all night. There is a trick to it. Don’t leave a show hot all night.
Koz
If the temp files were more than 24 hours old or you set CCleaner to clean Windows temp files even if less than 24 hours then that would happen.
The upcoming 2.1.2 release of Audacity will not allow you to set a temporary directory that file cleaners will act on.
Gale