Captain:
Most audiophiles claim that external audio interfaces will provide the best results for low interference, less noise analog transfers. However, there are some great internal sound cards from M-Audio (Audiophile 24/96), Echo Audio (Mia MIDI), Digital Audio Labs (Card Deluxe) and Lynx Studio Technologies (Lynx 1) that rival the sound of outboard audio interfaces. For affordability, you can't beat the Echo Mia with its balanced inputs and outputs. For greatly improved sound many professional audio engineers will take the Lynx 1 or the next generation Lynx 22 over more expensive outboard DACs. If you have a Rega Planar turntable, I am assuming you have a good preamp which you can connect to the balanced analog inputs of any of the aforementioned sound cards. Using a quality audio editor/recorder such as Bias Peak (Mac), Sony Sound Forge (PC), Adobe Audition (PC, formerly known as Cool Edit Pro) or even the budget-proced n-Track Studio (PC), you can record at 24-bit/96 kHz digital resolution.
Some responses included information about distortion originating from digital jitter. The Lynx 22 has an internal clock that reduces jitter and provides a very clean, quiet and coherent output through its high quality DAC. The Digital Audio Labs CardDeluxe was actually a Sterephile Recommended Component for a while. Obviously, these cards can hold their own. Unfortunately, some people get swept into thinking that everything separate somehow equates to best performance.
Beware of some USB audio interfaces as USB is not the best data bus for high resolution audio. USB 2.0 is definitely an improvement over USB 1.1 for throughput and stability, but they are both shakey for handling large streams of digital data. Firewire is a much better bus for handling music data streams, and there are some really nice Firewire audio interfaces from Mark of the Unicorn and Digidesign, but you must have a Mac for the best driver and software support for these audio interfaces.
Also, you may want to consider a second hard drive to store all your music. Remember that a computer's OS is constantly accessing the system drive during operation. Having a separate media drive should get you away from interference from the OS. A good 80-160 GB IDE drive running smoothly with a rotation speed of 7200 rpms, a memory cache of 8-10 MB and seek times < 10 ms should be a good place to start. You can also add an outboard Firewire drive with similar specs, and get great results.
I know a lot of people have recommended professional CD burners, and these are good units, but some of the AD/DA converters in these machines aren't as good as the converters in the audio interfaces I mentioned. On top of that, they'll only provide 16-bit/44.1 kHz resolution audio (the Alesis CD/HD unit is the only exception here). You'll also have stacks of CDs rather than an excellent collection of higher resolution tunes on your hard drive.