Just to clarify, are you looking for a CD player or a multi format player? Your original post says CD player. If thats the case, I think you are better off looking at something that plays CD's only. There's no reason to buy something like an Oppo that is designed to do a whole bunch of things that you will never use it for. More importantly, CD's need all the help they can get to sound good.
As far as getting a CD player or separates, that's a personal choice. Unless you are looking at something like Wadia or DCS separates, I prefer a single box solution. Generally speaking, with high end audio, things tend to get broken down into more separate, specialized pieces. (For example, instead of a receiver, you can go with an amp, preamp, phono stage and tuner.) If you look back to when high end CD playback was first getting popular, the general trend was just the opposite. To deal with problems like jitter, keeping everything in one box fixed a lot of problems. Of course, today, manufactures have come a long way fixing those problems, but for me, I still like a single box solution.
Unlike a lot of people, I have had very good luck with reliability issues. I've had CD players that were set on repeat for years just to break equipment in and keep everything warmed up. Never had a transport break. (Honestly, though, had I been more aware of some of the reliability issues that others were having, I would have shut them off, just to be safe.)
Some brands I would recommend, new or used, are: Ayre, Arcam, Wadia and Cary. I've had many others, as well, but the ones I list are my favourites.