help a Die hard ANALOG guy choose a budget CDP

Agree... a "decent" DAC can be had for under that budget (used).  At the minimum, maybe get a Cambridge Audio DAC Magic Plus (about $500 new), just to get a taste for it.

The computer necessary to simply run the program (Like JRiver) doesn't need to be anything special in terms of CPU, RAM or anything either, or can just be a laptop. 

Just kinda need a big hard drive full of music.  The computer is just to run the software from and organize the music really. 

I use JRiver on a cheap Dell PC (about $350 new) with 8TB of external hard drives attached to it and JRemote on my iPad Mini.... very easy.  Sit in your chair with access to tens of thousands of songs AND it will sound better than your CD player.

@fjn04 Yes, some of the brands you mention make nice stuff, but the Bricasti DACs and Lumin network players are well above your stated price range. Not to worry though. 
It's true like @audiofreak32 and @mesch say that running computer audio (from a PC or Mac) into a DAC is not that hard to do and can be an improvement with good software. I did that for a few years in my case with a Mac running Audirvana+
But for my money, the better sounding and wiser investment is in storing your library on network attached storage(NAS) and playing that music on an ethernet based network player such as the Sonore microRendu, Aurelic Aries, Aries Mini etc. with a quality linear power supply & that fed into the best DAC that you can afford. Supplement your library with Roon and Tidal streaming service music if that's your cup of tea. Many sonic benefits result from using a lower powered single purpose device in the listening room and isolating the music files via ethernet. High quality power supplies in the listening room can have dramatic impact on the digital gear.
The only reason to stick with a powerful PC based system is if your are a more hardcore PC enthusiast and you want to tackle running HQ Player and take advantage of its digital signal processing and mega upsampling options(a whole massive topic in itself & more complex than many want!).
To get a handle if this approach is a good fit for you I suggest reading Chris Connaker's and Michael Lavorgna's reviews of the Sonore microRendu and watching Hans Beekhuyzen's video reviews of the same and the Aurelic Aries Mini. Cheers,
Spencer

@whart This other post of mine hopefully addresses your suggestion. Thanks,
Spencer

@sbank -Thanks. FWIW, re linear power supplies, i was pretty surprised to see how much some of the audiophile ones were (maybe I should not have been). And many of those were limited to one voltage/current output. I bought a decent bench supply of the type used for testing/repair that has variable settings for both voltage and current, a large toroidal transformer, etc. Not a true high end lab quality model, but good enough for my purposes- I am using it to run an Acoustic Revive thingie right now. I can supply a link if anyone is interested. 

Running music direct from a hard drive, via USB will be more than adequate.  Using an ethernet setup does not automatically make better sound.  Setting up a NAS can be very expensive and is far more involved than simply connecting an external USB hard drive to a DAC.  The money would be mush better spent on just buying a better DAC.

I defy anyone to actually be able to hear a difference between hi-res files fed from an external USB hard drive and those sent via ethernet from a NAS.