Hey - let's really muddy the waters!
If you don't have tubes anywhere in the chain, the CDP is a great place to put them. Usually only 2 low-power (cheap) tubes that last a long time.
Preamp is also a great, easy place. Hey - I have 'em in both!
Tubes are one of the best things to ever happen to digital. Different tubes will help you "tune" your player to your system too - much more effective AND cheaper than using cables for that purpose.
My CDP is a modded unit from Modwright but there are killer choices OEM too. Check out the Unison Research Unico CD. Classy and great, for about $2k.
The only CDP I know of that uses a CD-ROM transport is the Creek CD-50 mkII. Creek reports that it reduces jitter considerably and the player is well reviewed. Computers generally don't have jitter problems, so it does make some sense. No tubes though.