Best Integrated Amp (for me)

https://www.marantz.com/en-us/product/amplifiers/pm8006

I had a Marantz PM8005 that I really enjoyed for several years before upgrading to tube. The current model is the PM8006 at $1100.  I would check to see if you can find a used PM8005 or PM8006 somewhere.  I sold my PM8005 for $650.

Rogue Audio sphinx is a great option for you as well. New they're like 1600 but there's at least one for sale on here.

https://www.audiogon.com/listings/lisab5i4-rogue-audio-sphnix-v2-hybrid-integrated-amplifier-black-w...

op

my suggestion of the hegel is solely for the quality of its amp section ... consider the dac and streaming features freebies

* * * * *

@audioconnection

op said -- "I’m looking to spend somewhere between $500-$1000."

johnny, if you have a used belles aria available for under a grand i would like to buy it :)

The Parasound NewClassic 200 Integrated is really nice. 
I got one 2 months ago and have now sold off my preamp and power amp....no regrets.
Its very musical, outputs a clean 110 wpc @ 8 ohms, mm/mc phonostage, bass management, a good burr-brown DAC and a back-lit remote that gives you full control over bass, treble, balance, sub-gain, even a sub on/off. I do a lot of low-level listening so the tone controls can come in handy. 
Parasound has been experiencing component shortages the last few months making this integrated amp almost impossible to find. It's supposed to be back in stock by mid-late Summer. In the mean time the one for $900 that Bkeske mentioned is a great deal.

I'm going to go ahead and suggest what I bought 2 years ago and it is still giving me great sound.

The Vincent SV-500 Hybrid Integrated. 

Simple looks in Black or Silver.

Slightly above your suggested budget but worth it in my opinion.