NAS/Streamer or server/player?

Get a synology NAS and a Sonore or Lumin U1.  Keep it simple.  Both will be a great roon streamer and the NAS should be RAID.  Way under your budget you listed.  

Added a Lumin D2 with Synology Ds918+ NAS and 16TB’s storage in conjunction with Roon Nucleus +.  Liked the Lumin so much I upgraded to the T2 when I added my Audio Research Ref6SE preamp.  With Lumin app you can play Tidal and Qobuz direct into preamp or amp which sounds better than going through Roon. Good luck and let us know what you end up doing. 

The difference here is in how the devices handle their jobs.  The digital front end needs to do a few things.  It needs to access your local files, deal with a very volatile internet and the decompress/unfold your files as it serves data to the DAC.  

The first step managing files and dealing with the internet is very processor intensive.  This is where a server really excels.  

The rendering (decompression/unfold) is far less processor intensive and many manufacturers argue that to much power here introduces noise.  

All of this has to be clocked and synchronized with the clock in the DAC.  

Given these points above, I fall firmly in the server/player camp.  I don't love the pure streamer approach nor do I like a single computer/server approach though I feel a single server outperforms a single streamer, especially at the high end.  

I like splitting things into different parts.  This is what Antipodes does in their higher end servers.  The K30 and K50 have two computers, one that is higher powered than the other.  Another approach is to get a single server (Roon Nucleus, Antipodes S40, Antipodes K41, etc...) and pair it with a Roon Endpoint like a Bricasti M5 or Weiss DSP 501/502.