Cambridge Audio CD Player Has Died

Thank you, everyone, for the responses. I certainly am well aware of the pros & cons associated with the two options. And, of course, personal preferences enter the equation.
So, the rest is up to me. It's time to do my homework & weigh the options. If I have any further questions, I feel confident that this forum is an excellent resource.

Well, it's time for me to explore whether to replace my dying Cambridge Audio CD player with another standalone CD player or with individual transport & DAC units. From all of your previous comments, I can assume that some of you are immersed more deeply in the audiophile world far than I. So I would respect your recommendations on specific brands & models of transports & DACs that pair well together.
Here are a couple of parameters I would like to stay within: (1) units that will complement the "musicality" of my Audio Research tube preamp and (2) a combined price range of $600 - $1,000. However, I would be willing to extend my price range if there is a significant increase in audible quality.
Thank you in advance for your help. Much appreciated.
Kit

Two very nice players are Marantz or Yamaha ( Crutchfield.com.)Then add a dac later.
If you stretch your budget a bit a Cambridge transport (Audioadvisor.com)and a Border Patrol dac(LTA.com) is a great combo.And a digital cable of your choosing.No affiliation with these companies,just some places to browse as you research.
I'm auditioning a Parasound dac right now that I really like except the upper midrange has a very slight glare that is bugging me.I have a new cable ordered that may clear that up,fingers crossed.Other than that one area it does everything right,silky and detailed.

+1 for Marantz or Yamaha, also the Tascam 200 

If you pursue separates, the Oppo 103 plays well with a Schiit Modi Multi, using Blue Jean 75-ohm digital coax.