Nicodemix: lots of answers to your question since what you’re asking is just for a server, if I understand your question. Price is always a variable.
A few options I can think of off the top of my head: your computer can serve as your server. I use JRiver software. You can control the JRiver software from a JRiver remote on your phone. All you’d be paying to is a JRiver fee ~$30. This is what I do now. It’s works just fine. No complaints.
Another option would be something more audio dedicated. If you don’t need cutting edge technology I would look into a Naim unitiserve. It’s not their latest one but will meet your above stated criteria. I have seen them for as low as $800 on Audiogon. I think I will go this route in the near future. I have a naim preamp/dac/streamer now so I believe it will work together within the same app.
There are others out there but all much higher in price. Wyred 4 sound makes a server/streamer, $3k. Aurender makes some well reviewed servers starting at $2k. Melco is another name to look into.
Can’t go wrong with Bluesound Vault but it’s a streamer too. Good user interface, $1300.
Hope this points you in the right direction.