help a Die hard ANALOG guy choose a budget CDP

@violin  AMEN!  I am enjoying the 30th Anniversary SACD of Goodbye Yellow Brick Road on my SA-8005.  Rediscovering Elton.

If your Sony has a digital out, I would choose a HQ DAC like Schiit.
The Sony will spin the CD’s and the DAC will be updated for a much better sound. I tried SACD, was not impressed and not too many discs. Also I have used Spotify and Tidal. You can get very good sound from both with a good DAC running.

If I were to buy a CD/SACD player the Sony SCD-XA5400ES would be at the near top of my list.

I have run a Rega Apollo into a Schiit Bifrost Uber for improved sound.
I also run a Sony ES cd player into a Benchmark DAC1 for improved sound.

Just an idea....

I would get a good DAC and then an inexpensive transport. You can use the DAC with streamers and other digital sources going forward.
OTOH, the Oppo 105 is a pretty good DAC and is in your budget and can perhaps be used as a streamer (I own one but haven’t tried it for that).
I don’t know if the Oppo fills your ’analog’ criteria. The are no pops and clicks, speed stability issues, or dust bunnies hitching a ride on a stylus. Nor are there warped lps that gave been sitting in a basement molding away for the last 40 years that will play on it. You do get a significant amount of detail without an overly clinical x Ray feel.

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