Cost-effective integrated

For new, the Parasound NewClassic 200 is pretty nice and ticks most boxes that anyone could have.

For used, there's a Classe CAP-101 here on Agon for sale.  Those are pretty nice, as well, with minimal features.

NAD and Cambridge Audio also have some nice offerings around $1000 that seem to get great reviews.

Rega Brio is right at your price, and you could save some money by finding a used/demo model.  Wonderful, engaging sound.

Thanks very much for the suggestions... interesting that NAD comes up - I had a 7120 receiver when I was in school.  No tubes, but you did have to keep it stoked with coal!  Seriously, though, that piece lasted about 15 years and I was very happy with it, so I will explore that option - and the others mentioned so far. I really appreciate the insight!

I bought my Jolida 302CRC for $600 a few months ago. It’s pushing some 150lb speakers and manhandles them up to 90db or so. Tons of texture and tone and just great sounding. For under a grand I would look at Jolida if your into tubes.

I have a Musical Fidelity A1008 (a 6k integrated from 15 years ago) for just over you budget on the way. 

In this price range NAD would be a good choice.