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

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

For fuller sound at lower volumes, I'd suggest using part of the budget for a small subwoofer.  I have run one in my secondary home office rig for years and it allows me to have great performance at any volume but also the ability to run bookshelf speakers on stands, making the room feel larger not as cluttered, not having to worry about pulling larger towers out into the room to breathe, etc.