the most idiot proof way to do it is to get a CD ripper/streamer/storage in one. The Bluesound Vault2 would fill your need. For about $1200 it will store about 5 times your collection size in its 2 TB HD after ripping them to flac. The app to control works well and you can also use it for Internet Radio, Tidal, and Qobuz, and a whole lot more It has an internal DAC but your Wadia will prob ably beat it. You already have an pre amp and amplifier so I am not sure why you are looking for a product that has that included.
You may want to retain the CD player as a backup in case something goes wrong with your stream or your internet connection, depeneding upon the quality of the Internet connectivity where you are relocating