help a Die hard ANALOG guy choose a budget CDP

If you have that kind of budget, don't buy any CD player at all.  A good DAC with destroy the same priced CD player and those at 5X their cost, period.  Stop spinning CDs.  Moving parts, jitter, optics, laser, motor, etc.

Buy a simple program like dBPoweramp or similar, rip all your CDs in at at least 24/96k FLAC or WAV and prepare to lose your mind when you hear them through the right DAC. 

My Eastern Electric tube DAC ($1,350 new), a Line Magnetic tube DAC or used DAC from Chord, Mytek, Ayre, Auralic, etc.

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.

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.

Lots more work/cost for not much benefit...

My point is...

If someone is spending $XXX (say $4,000) total on a front end source...

There is NO WAY any CD player will touch a DAC at that same price.

I stopped spinning CDs about 6 years ago and never looked back... it has been proven to me time and time again by demonstration and in the transformation of friends' systems from CD to DAC.  Getting up to search for/change CDs is more time consuming than sitting in a chair with an iPad with access to 25,000 songs at your fingertip.

"... has the potential to sound better". 

Ummmm. more like NO QUESTION it will sound better.  You would need to spend AT LEAST 3-4X (IMHO) to better a DAC at the same price.

If you spend $1,200 on a CD player or $1,200 on a DAC, there will be NO comparison.  Once you take all the moving parts, laser, flutter, vibration, etc. out of the picture, you gain so much.