DAC recommendation

Border Patrol Dac is a bargain at that price point and sounds fantastic and if you don't have a SPDIF cable, get Steve's Ref Digital Cable from Empirical Audio.

Wig

@wig @audioengr looks cool but appears to be 5x or 10x times my budget. Am I missing something?

it certainly is described as having the traits I’m looking for - I like my CD players for their involving, analogue-like sound. So I’m wondering if there’s a DAC for that price... thanks!

Unfortunately, as you go up the model line, the better the sound reproduction.
I have owned almost all the Schiit line. From Modi to Gungnir.
The Bifrost Multibit is probably the best buy, but at $450 used, a little over your budget.
The Modi Multibit is certainly in your budget, and I think you will be happy with it.
The thing about DAC's is that they are moving at a fast pace regarding sound quality reproduction, so I try to find a manufacturer who will offer upgrades.
Both Ayre and Schiit do so, and are the ones I buy.
B

At the price point you've specified and if you remain unsure after reading other recommendations in this discussion, an Audioquest DragonFly Red will set you back around $200. Plus, it's highly portable (about the size of a USB thumb drive) so if/when you get something more refined/sophisticated, you can use the DragonFly with your phone or laptop. It's been favorably reviewed by several experts. Audioquest also releases free firmware upgrades and the Red does the second MQA unfolding, too.