Looking for suggestions on speakers and an integrated amp for a second system.

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.

My main concern is sounding full at low volume level.

IME, that's a hard one, pal.

I have that problem in my office system and use the fairly high efficiency single driver, fostex based, Brines 2000.  They are no longer made, but single driver is a thought, and there are numerous options out there I bet would sound pretty good at low db.

My main concern is sounding full at low volume level.

Out of favour in amplifiers for quite some years, but when understood correctly a "loudness"  feature is useful for fullness at low volume. Vintage rocks!

It shouldn't be used at volumes other than fairly low or weirdness happens.  There was some discussion here within recent memory.

Here's a link to a technical discussion. including recent developments.

@noske Yamaha still has this feature in some of their Mid-Fi Integrated's