Need a new CD player. Suggestions please.

Stay with major brands like Marantz, Rotel, or Musical Fidelity in the under $1000 price point.  If you buy pre-owned, be careful.  Many audiophile manufacturers are no longer supporting disc format equipment.  Lasers have a usable life.  So parts and support may not be available.  Check with the manufacturer before buying pre-owned models. I learned by experience with a Linn Unidisc 1.1.  
 

My strong recommendation is to go with a server/streamer and either stream albums in your collection from Qobuz or Tidal, and/or burn and upload your CD collection.  I believe you will get better SQ in this way.  You may need to up your budget to $1500 to get a pre-owned Aurender N100H, Innuos ZENminni, or equivalent.  Personally, I prefer the Aurender house sound.  If you up the budget to the $3500 range(within you $3000-$5000 range), sound quality will improve proportionally if you get a pre-owned Aurender N200.  At reduced SQ compared to the prior recommendations, go with a new Bluesound Vault server and/or Node streamer.

Good luck.  

I have a Sony. Plays every thing and streams video.. Only issue Sony discontinued it. There's some still available as their price was somewhat high.  below is what is available from amazon

 https://www.amazon.com/Sony-UBP-X1100ES-UHD-Blu-ray-Player/dp/B07RN2RM5Y/ref=sr_1_3_so_VIDEO_DISC_PLAYER?adgrpid=1338106215446391&dib=eyJ2IjoiMSJ9.DhudoQZezlXtW25VKAYqCsNjgaMJjILiVTSPLG5SzwPK0b_FHNe2ZH1tYXmhz1jnlncDdsrUnfi__zt8agSZDvjD3VNJOAgTF3CqINcySnS7lNtQ6r2dA9poXPEWaDZrSo6wVl7btpBSIIokiL5fhlI_2Xm4JjTPGPqGm3RznuLy6AGXhppliPL6uwz7aA-LfA4vkWXdFbzew21s6iYBK3b4nt7oPCrTuSgL4m1qasI.eoWHjbomLBWybw1RqBWr6j9HXYqF8lQJP4Z9R1ZjIHg&dib_tag=se&hvadid=83631853456764&hvbmt=be&hvdev=c&hvlocphy=100010&hvnetw=o&hvqmt=e&hvtargid=kwd-83631984203462%3Aloc-190&hydadcr=14415_13350680&keywords=sony%2Bubp-x1100es&mcid=2056fa25329c307385a4a81ebf11ede4&qid=1758559662&sr=8-3&th=1

Thank you for all the replies.  Keep 'em coming.  My range is not 3 to 5k.  I asked for suggestions of 1k or less.  Not sure buying a used CD player is a good idea.  So far the Advance Paris units seem very promising.

If you decide to go the separate cd transport and DAC route don't go the cheap transport route e.g. the Cambridge or Audiolab mentioned above , they are okay but you will be under optimizing the DAC.  I had the Cambridge and moved on , it was pretty clear once I did. 

I haven't used a Canor or Gato CD player but Atelier 13 (I am not "affiliated" with them just a customer)  has deals on each one a demo, one a stock rotation a bit over $3K each.  You can find reviews online if interested.  Links below, just need to scroll to see the units

https://www.atelier13-usa.com/dealer-audio-component-demo-sales

https://www.atelier13-usa.com/new-dealer-audio-stock-rotation-sales

This is a great time to just abandon the CD and move to streaming. Depending on your DAC, if you are going to spend that much money... I would get the highest quality streamer. You'll get access to about very CD you own and a million more for ~$12/ months with Qobuz. There is no innate sonic advantage to physical media. I'd start looking at Bluesound streamers, and consider a used Aurender.