Comparing these CD players with my gear...

An Eastern Electric Minimax is within your price range if bought used. It is tube based and is as close to analog sounding as any single unit I have heard. Good luck on your search. 

mgreen27

"Why not look at the analog section of the dac as well? I think you’ll find all the players mentioned use dac data textbook I/V stage and output stages, which are just opamps."

I’ve owned 3 of the players on the OP’s list and I have a fair amount of time with 2 others. They all sound different. Audio is hands on. If you want good sound you have to be proactive. That means listening to as much gear as you can. If you make buying decisions based on spec sheets, that’s what your system will sound like. A spec sheet.

This is why most of the one mentioned have text book I/V and analogue stages, nothing special.

But if you really want to be hands on and have the ability, you can do a far better feedback free I/V stage and better output buffer than these text book ones that OP is choosing between.
Here is a link I started over at DiyAudio on a better I/V stage for dacs and cdp's which gives a far better sound than the text book stuff.

http://www.diyaudio.com/forums/digital-line-level/227677-using-ad844-i-v.html

Cheers George

@mgreen   In a world with loads of brick and mortar come listen to it establishments what you said would be THE way to go, however in my "neck of the woods" (literally) there are NO audio shops to listen to gear.  My last major purchase, Vandersteen Treo CTs involved a 6-7 hour round trip to make the purchase.  In that particular instance I was buying speakers from a manufacturer whose speakers I have owned for the last 30 years.  I knew pretty much what I was getting without first hearing them as available reviews and discussions with owners confirmed what my relationship with Vandersteen Audio had me believing.  Fortunately all is well as they have turned out exceeding my expectations.  I do envy those of you fortunate enough to have audio emporiums in close proximity.

Thanks to everyone and all your comments/suggestions. Based on what I read (both here and in magazine & online reviews), as well as comparing the other players listed to my previous players; and considering my budget, availability and personal curiosity, the two finalists are:

Naim CD3.5
-or-
Theta Miles

*Cast your Vote!*

Some prior player background:
My most recent player was a Rega Apollo. Before that, it was a Micromega Stage 3. The Stage 3 was a fantastic sounding player, but those old units are plagued with issues--everything from display to output sound. It was a very smooth and refined player. The Apollo was great too, but not as refined as the Stage 3. What I noticed on the Apollo was the ever so slight upper treble pronunciation. What the Rega had over the Stage 3 that I liked was the sense of rhythm and beat. I found myself foot-tapping more when playing the Apollo. Both players were great with imaging & soundstage. The Apollo R is out of my price range, as it the Micromega. As for music, I listed to pop, rock, metal, ambient, classical. Though most of the time it’s pop, rock, ambient/atmospheric and some metal. I know I indicated I used to have a Miles previously (two in fact). However, I never used it with a dedicated preamp; therefore never heard it with the volume control function deactivated. They were always used being connected directly to a amp. I've since come to learn how important a good preamp is to the sound of a stereo system, and now a wonder what the Miles would sound like on the Creek? But, at the same time, I've never owned a Naim and have heard, and read some wonderful things about all of their players. I do love the british-sound.   

*Cast your Vote!*

Naim CD3.5
-or-
Theta Miles

*Cast your Vote!*

For me neither as these are both "Delta Sigma" (bitsteam) based converters.

I love the sound of "Multibit" converters when converting CD (RedBook) 16/44 or 24/96. They have better jump factor, which gives more involvement to CD, and are bit perfect. Delta Sigma converts Redbook as a facsimile of the real thing.

Quote from MoJo Music:
" When a PCM (CD) file is played on a Delta Sigma or Bit Stream converter, the DAC chip has to convert the PCM to DSD in real time. This is one of the major reasons people claim DSD sounds better than PCM, when in fact, it is just that the chip in most modern single-bit DACs do a poor job of decoding PCM." 

Cheers George