I put together a pretty good digital system for my office about the same size as your room, that meets your budget. The system sounds great, almost as good as my main rig but really, with the bookshelf speakers, its only for relatively near field listening.
It consists of a Pro-Ject S2 Ultra Streamer, a Pro-Ject S2 Digital Pre/Dac, and a Pro-Ject Amp Box. I used all my 'second' cables (i.e. those I replaced for better cables) which are OCC 6n silver-plated speaker wire (ELF Silver Surfers), a Wire world USB (ultra-violet) and bespoke LPS units for the Streamer and Amp. Three of the pieces were pre-owned. I use the steamer as a Roon endpoint from my Innuos Zenith Mk3 Roon core, but the Pro-Ject software works fine and lets one use it to stream Qobuz or Tidal (possibly others) without Roon.