help a Die hard ANALOG guy choose a budget CDP

Interesting question, in part due to the claim about how good the PS1 is.  I own two of the recommended PS1s, picked up for $5 each from a consignment store.  I find them to be terribly inaccurate CD players, with a bloated midrange, rolled off highs, and poorly defined lows.   Very easy to pick out in a blind comparison, due to how much they alter the sound as compared to a high quality CD player or DAC.   When I played my favorite demo cuts through a PS1 into a high end system, I was shocked by how much they were altered. 

A good CD player, and several have been mentioned above, will be far more accurate and defined, capable of producing a beautifully deep, nuanced soundstage. 

@fjn04  As someone who has been posting here since the beginning without a commercial interest and in good faith, let me respectfully make a rare statement that I am not sure that much of the advice posted in this thread is current good advice. The exception being to invest more in a better DAC, which will be a good investment regardless of which digital source you choose now & in the near future.

I get the feeling that many of the replies could have been written 10 years ago, and the perspectives don't reflect much experience with the latest in digital sources. Digital network players, fully optimized computers(including special software and upgraded power supplies) and other "appliance" players with built-in hard drives all can and usually will give you superior results to most conventional disc players. This is a more complicated topic than many and much has been written about players from Sonore, Aurender, Aurelic, Melco and others that IMHO turn the digital music paradigm on its head. 
IMHE, a modestly priced network player, music stored on a NAS and a good DAC can provide staggering improvements in sound quality and increased convenience vs. disc based solutions. It's really worth investigating! I won't derail your thread with specifics about any particular products. 
If any of the earlier posters here have compared such products and prefer the sound of their disc players, I apologize to you and look forward to hearing why your prefer them. If your advice is based on the inconvenience of ripping discs, I'd encourage you to overcome that challenge and take the plunge. Cheers,
Spencer

@sbank : Spencer- you should start a new thread that helps demystify this for readers. I love my records (even some that were natively recorded in digital and/or pulled from digital masters), but there are some obscure records that have never been reissued and are simply unobtanium as original pressings--(one is a four figure record that a friend had remastered on CD years ago. I just want to listen to the music, not make an "investment" in a collector’s item). I’ve stayed out of the digital arena largely because I believed that I could never achieve what I get from analog without spending a comparable sum --and felt the money better spent on the analog side, but I may be ready to take the dive simply because a lot of the material I’m chasing is very hard to find at a reasonable price. Your thoughts might be helpful for a number of readers.
Thank you.

There is no need to spend 1300 to get top shelf sound...

In your opinion which players define this 'top shelf sound'...?

Spencer-  I think a streamer is what I want to explore. The word THINK in that last sentence, is because I want to research if a streamer has better sound than a CDP in the same price range. In my reading, I've stumbled across the brands you mentioned, along with Chord, Lumin, Bricasti, and Halide. Sure, I'd like to play my 100 or so CD's, but not at the expense of lesser sound quality. This is the door I wanted to open. Perhaps having just CD player in my initial post was a tad incomplete . I apologize for that, and thanks to all for your suggestions. Again, I'm  a bit out of touch with CD players, but with streaming, totally green.