Computer, CD transport or Network Player?

I can't answer your question about DAC implementation. But.... My buddy Ghosthouse suggested a number of years ago to try out Spotify. At first I treated it as you do: like music, then buy CD. Now I just go to Spotify and listen to it there. My CD collection is getting smaller now and I'm fine with that. The best CDs stay but those that aren't getting play go to the car for evaluation and if they don't pass the test they get added to the pile that goes to Fingerprints in Long Beach where I sell them. I usually pick up a some new CDs, but many less than I sell. I've also shelved ripping all my discs to an NAS. Lots of work for little return with online sources like Spotify and Tidal. Of course YMMV and this is but one mans IMO. Have fun!

I have seen claims that SSDs sound better than HDDs, also that the LCD drivers in a laptop create more noise in the digital stream than say a mac mini (more room between components, so the inverse square law helps quite a bit).

What I have not seen is actual measurements or reliable listening tests (blind, randomized, adequate sample size, etc.).

BTW, I am a WiFi type guy also.  It also breaks ground loops and is convenient.

Some problems are only going to be of importance if you are spending many thousands of $$ on a system.

I once heard a demo in a friend's home of HDD vs. SSD, same music file.  The differences were not subtle, with the SSD offering much better everything.  This was a good, but modest system with bookshelf speakers, and plenty of tweaks.  I made up my mind that if SSDs get a bit cheaper, I will try to replace the HDD in my Vortexbox appliance with a SSD. 

I would think a non moving parts transport would be superior. But just wonder about the pros and cons of an SSD versus network player. How would a DSD DAC fit in this mix? Would it increase SQ?

Any of the three will work.  My personal preference by far is a silent Windows based PC.  Doesn't look like a PC if you choose the right enclosure.  It can be built for about $1,500 including an audiophile sound card, graphics card and very good Blu-ray optical drive.  Due to driver restrictions for the sound card it has to be W7.  Sounds phenomenal and no noise what so ever.  Allows you to do everything on your list and then some.  Personally, I fought this approach for quite a while. I am totally happy that I finally did this.
If interested I can give you the Email address to inquire and obtain the sound card. I can give you some advise on components as well.
Best of luck!