I just finished analyzing, evaluating and comparing several media players. To my knowledge, there is no media player that meets all of the requirements you listed in your post. There are players which will play many different types of files (more than the average player) but they don't display album art (as one example). As to the question of what the best player is becomes a matter of personal taste. To give you a few examples of my personal tastes regarding media players, whether the player displays media art, has the capability to display song titles from a CD or is capable of burning a CD are all aspects which are completely unimportant to me. If the media art of a particular album is that important for me to see I can always do an internet search for it. And I have programs which do a much better job (faster and better quality sound) of burning a CD than any media player's capability in this regard. What is important to me is the sound the media player produces.
One player that will play almost type of file is the VLC Media Player. It even plays flash files. It does not, however, play APE or REAL files. Actually, I have never used APE files and I rarely use REAL files. And, I have never come across a file of interest to me which was an APE file. They are most certainly not the most common of files. If there is so much of a challenge in finding a player which will play the APE files as well as meeting your other requirements, who needs APE files? I am sure you will be able to find the songs in a format which will be more universally compatible to media players. I would suggest finding a file converter (some are freeware and easy to find on the internet) and converting your APE files.
If you're interested in knowing what the best sounding players are, let me know.
I hope this helps.