good/best CD player with variable out

Try the new Cary Audio CD-308T. It features a tube output stage with variable gain. Does upsampling too!

It can be a very good idea (if you like the direct sound). The most important thing to consider is the quality of the volume control on the CD player's variable out. A poor volume control will sound worse than a decent preamp. Do a search on CD player's with volume control, and you should find plenty of previous threads on the same topic.

I agree with Phild.
A player with an analog variable output is IMO far superior to those with a digital volume contol.
I have found that there is a need for the cd player to have sufficient output to drive your amp.
I run a Resolution Audio Opus 21 direct to my Lamm mono blocks.
There are a few units out there that seem to do it all. The Levinson 390 the Audio Aero Capitole come to mind. I've owned all three and the Resolution Audio is my prefence and is less than half the costs of others in their class of excellence.
I have yet to put an adequate pre amp and interconnect in my system that reveals the same depth of detail and harmonic richness that comes thru without any pre amp and I've tried combos well into five figures in cost.
At 3K the RA Opus 21 is a no brainer.