Basic Technics turntable to high quality AMP to shielded RCA to stereo mini-jack converter cable to WHICH Digital recorder?

My three main digital recorder choices:

• 1 year old gaming computer (onboard audio "SoundMax HD Audio" on Asus P5K motherboard, running with Intel Core Duo 2.66 GHz CPU)
  
• 5 year old general purpose computer with separate soundcard (SoundBlaster Audigy LS, "SB Live 24 bit", running with AMP Sempron 2600+ CPU)
  
• XM MicroMemo iPod nano Voice Recorder, recording 24 bit stereo

Hoping:
Someone suggests the iPod recorder is good enough, because although the attachment would cost a bit, I wouldn't have to move a computer to the stereo with the turntable. Might be neat to try to record some ocean waves with it too. Probably worth it over time.

Remembering:
Digital recording I've done in the far past with computers was good enough, but I DID have to be careful not to run any background programs or a few blips could sneak into the recording here and there. Maybe the newer, faster CPU's don't run into this problem, so long as a virus check (or some such) doesn't start?

Background:
I'm thinking about transferring about 100 tracks off of vinyl onto CD-R. Probably more in months to come. First batch pretty much ONLY for my 79 year old Dad, who (I'm pretty sure) can't hear minor imperfections in recordings any more. Note: I did notice someone talking about archival CDs and their limited shelf life.

Any pointers to free or inexpensive programs for cleaning up the recording (can Audacity do this?) would also be most welcome. The free sound-cleaners I used in the past (more than 5 years ago) numbed out the sound so much that I used uncleaned recordings.