Burn-in? Huh? What Burn-in? Forget about that issue.
Your budget is right in the sweet spot for my great DACs, new or used. If your source is limited to playing only Redbook CDs, the general opinion, with some exceptions, is to use an R2R (resistor ladder) design DAC. Schiit multibit type DACs seem to be a very popular option but there are many others out there. Denafrip Ares is another choice and should be within your budget. I'm using a DACmagic Plus with an external aftermarket power supply to improve the SQ of my old CDP and the total cost was around $500. By the way, your system is more than modest and is quite good. A good Good luck.
Gustard X20 Pro with USB - $869
Audio-GD NFB-1.38 (ES9038 Pro, Amanero & TCXO built in.). Around $800-850 shipped to USA.
Audio-GD R2R 2 (if you want resistor ladder DAC) - Around $800-850 shipped to USA.
If the DAC is bought new, then you may have to run the DAC for about 100hours to burn in components (such as wire, capacitors, etc.). This is a controversial subject (see shadorne's comment), but I have experienced burn-in many time. The sound can change over the initial 100 hours until it settles. The changes could be bad sounding at times (could be bright/harsh/messy). It's up to you to decide on whether this is a real thing or not.
I kinda agree with shadorne in that streaming audio can be very rewarding. Roon and Tidal can give you many, many options for enjoying music. There are a number of streamers with DACs and if you are wanting to explore MQA you must get one that will unfold and play those codecs (files). Some audio brands have decided to include a MQA decoding, many have not (including Schiit). Needless to say, even without MQA a well designed DAC will sound fantastic. I have gotten away from using my computer to play audio and use two dedicated digital music sources, my CD player with an external DAC and a Bluesound Node 2 for streaming and accesssing all my digital files on a NAS.
A few nice looking units on here in your price range, no affiliations with any buyers.