What difference would the XYZ DAC make?

I've spent some time searching and reading past Audiogon, Audio Asylum and Audio Review threads on DACs. While the comments are informative, they tend to fall into three general groups -- the "I own the [XYZ] DAC and it sounds great in my system so you should get one" self-validation group, the "[XYZ] DAC is detailed and images well" technojargon group, or the "Don't waste your time with the [XYZ] DAC, I have an [ABC] DAC and it just flat blows the doors off of that outdated old [XYZ]" in-your-face group. All are at least somewhat helpful, but... I listen mostly to small jazz groups featuring guitarists who focus on subtlety rather than slam (lots of Jim Hall, Wes Montgomery, Pat Metheny and Joe Pass), although I also listen to some classical, rock and folk. My system is nothing fancy -- a Cambridge D500 CD player (the original one, not the SE model), playing through a NAD C340 preamp section, a NAD C270 power amp, and Vandersteen 1b speakers, connected with MAS ICs and Signal speaker cables, with a Cardas power cord for the CDP. I tend to go for a warm and musical sound more than a clinically neutral or hyper-detailed sound, and value natural musicality above other characteristics. I do also look for clarity, detail, imaging, bass and treble extension, and pace, rhythm and timing, though. These are all things that I think I can recognize if and when I hear them, because I've been playing and listening to music for a long time. A used DAC seems a realistic place to start in taking this system another step further. We're talking units that would be cost-proportional to the other equipment:
-- original MSB Link DAC, unmodified
-- Link DAC III with Modwright mods
-- Cal Labs Sigma II tube DAC
-- Channel Islands Audio VDA-1 DAC
-- McCormack DAC-1
-- Theta Pro Prime or Basic DAC
-- Van Alstine Omega III, Omega IV or OmegaStar DAC
No helpful suggestions to try a Wadia or the latest Cary, please. I'd probably like the sound, but it wouldn't make a lot of sense in the context of my system and budget. No sneers warranted either, since my two kids in college are both higher priorities than my audio toys. Just straightforward answers (or scintillating displays of erudition) in response to two simple questions:
(1) Based on your personal experience, in what specific way is the sound of my current system likely to change with one of these DACs?
(2) Which of these DACs, or others available used in the same general price range, do you consider most likely to improve the sound of my system in ways consistent with my tastes in music and sonic characteristics, and why?