Which integrated amp do you suggest?

You won’t find a better integrated for $600 than a used Yamaha A-S801 or a new A-S501. They have a dead-quiet noise floor and their power exceeds published spec at well under 1% distortion for full bandwidth. They’re reliable and even 2 ohm stable. Bass extension and definition exceeds that of some ~$3K integrateds. Some competitors should be embarrassed really.

I think you’d be very happy with a Musical Fidelity M2si from Upscale Audio for $599. No DAC, but you could grab a Schiit Modi for another $99.

I have a fair amount of gear, SS, tube, separates, integrated and I keep coming back to my Peachtree Nova 220SE.  The DAC sounds great, it is compact and cool.  Underwood has some NOS at $1,000, but Peachtree has other models with less power that you could get used in your budget.  

Cambridge Audio CXA80. You can get one for $999 online. It is awesome and lots of power. I use a pair of Wharfedale Reva 3s with it. It has a built in DAC which I think is decent. Especially for TV use. I would get something like a Bluesound Node for streaming and DAC. You will need a separate phono stage, but you might already have that. 

The Cambridge can use a separate dongle you plug into the back that can do blue tooth. So easy streaming of Tidal from your phone, if that’s what you want to do. I have not tried that though. 

Jason

Oh I forgot to mention that I tried an Outlaw receiver from Music Direct before getting the Cambridge CXA80. No comparison really. 

Sure it is a jack of all trades, but a master of none.