In general...
On the software side, the better the recording (higher bitrates or lossless audio) the better the sound. Get or make the best digital copy you can.
Also, if you want to use equalizer or make changes to the sound, its best to do it in the digital realm.
Hardware...
First: 0s and 1s in your digital file (mp3/oog/wav/etc) needs to be translated to analog signals with a Digital-to-Analog Converter (DAC).
Second: The analog signal then sent to a preamp/headphone amp to adjust for volume.
Third: The analog signal is reproduced into sound through your headphones.
Soundcards have DACs and preamps built into them. The "headphone out" analog signal has been adjusted for volume already. You can also get a unadjusted analog signal through the "line out" straight from the DAC. You would plug in your Corda Arietta to the "line out".
There are some excellent soundcards with very good DACs and headphone amps. But, the bad electrical environment inside a computer deteriorates the sound card. The ideal solution is to move the DAC and amp components out of the computer and electrically isolate it from the computer.
In order of importance on final sound quality for a computer setup (assuming the components are not absolute crap):
1. Quality of recording
2. Headphones
3. DAC
4. Amp
5. Soundcard/computer digital output
6. Interconnect Cables (IC) - analog
6. IC - digital
6. Power Cables
Since you already have headphones, amp, and tunes on your computer, the next best improvement is the DAC.
Lots of these around, do a search. 2 basic ways to move data from the computer to the DAC. Optical/Coax connections through a soundcard/on-board audio or USB. USB DACs are getting more popular but there are more choices in traditional DACs. USB also gets into latency issues, CPU overhead, etc.
Going Optical/Coax, ideally you want move data without error and timed correctly. Bad timing is responsible for jitter. A dedicated "bit-perfect" sound card will do this well. The optical out of the back of the computer is pretty decent too if all it does is move the data. In general, sound cards inject less jitter than on-board audio.
The last bit of hardware is interconnects and power cords. YMMV. Give them a try when the major bits of hardware are in place.
A CD player or CD transport is useful if you just want to play a CD and not bother turning on the computer. The transport's main purchase is to read the data off the disc and move it to the DAC with as little jitter and error as possible. Data error is rarely an issue these days. A cheapo DVD player can act as your CD transport for a start.
In effect, your computer is a realy big transport.
