CDP or DAC?

OP, at your budget you have outstanding alternatives.  I would favor the transport-DAC route since DAC technology evolves and every few years a new development may strike your fancy.  Also if you ever decide to add other digital sources such as a streamer then you are set to go.  I would spend 1/3 on the budget and 2/3 on the DAC 

It is a very interesting question, since there are not many brands that are still producing and selling cd players.
Your choise, to name the few obvious ones, could be between the likes of Accuphase,Burmester, Dcs, Esoteric, Luxman, Metronome,Meridian or Luxman (some others as well, I guess)
I had similar dilemma recently and I have choosen single unit, Burmester 089.(had Metroneome, Dcs and Burmester before, as well)
I would be very curious to read any ’shoot out’ between single players and combos that are in that price range.
I guess that only by comparing them you will find out what sounds better for you.
I shop at the dealer who holds many brands and who gives the opportunity to try the units at home.
At one point I was considering Rockna Dac and some transport.
His advice, in my case (my collection is mostly jazz from 50’s and 60’s) was that for ’my’ music and that ’production’ ,dedicated red book cd player and not dac, is ’better’ solution, since many of dacs sound best with dsd, hi rez or other and were not made to play the rb primarily.
Also, not many really 'high class' transports are there to be found as well.
Than again, maybe he was just trying to sell me the cd player, as it is a not a much sought product now,ha,ha.

Thanks for all the great input.  Keep them coming. 

If you want to get close to analog I recommend an Audio Research CD9se. This is the best sounding CD player / DAC I have heard. The tubes allow for a wonderful midrange bloom and natural analog sound. I actually did a side by side comparison with a DAC costing $5K more and actually preferred the natural sound of the CD9se better.

ARC stopped manufacturing them recently because the company producing the transports stopped making them. But it should still be possible to find one, or used.

@ghdprentice You've pretty much hit on why its a crapshoot buying a CD player these days that transport goes and it's a boat anchor.