You have an advantage. You have not yet tangled yourself in the worthless opinions(s) by audiophiles, or so it appears. Realize, that the overwhelming vast majority of audio claims are bogus. They have no grounding in real perceptual research. You merely need to buy a CD player with decent quality that will be reliable and has the features that you so desire. More than likely, it will be a transparent device regardless if you use the digital or analogue outputs. However, realize that psychological factors play a role. In most cases, an expensive, reputed name brand, impressive looking device will seem like it sounds better, but this is a product of known human subconscious bias. Whenever this has been subjected to double-blinded, volume level-matched tests, the outcome of such cases has always been that of chance ( no better than guessing), except when a defect or intentional designed distortion was present on one of test pieces and readily measurable. Also realize, that the mere mention of double-blinded testing or other such things often upsets audiophiles, and they will go into baseless diatribes. Simply, it does not agree with their uncontrolled listening experiments and purely speculative opinions. Some extreme audiophile forums even forbid the discussion of properly bias controlled listening tests.
The main part to invest money in for audio in order to get substantial improvements is the loudspeakers and room acoustics. Period. Sufficient amplifiers, sources and pre-amps are cheap in comparison.
As for video, that is another topic entirely.
-Chris