Which integrated amp do you suggest?

+1 Yamaha, another happy customer of  Yamaha over the period of 2 years. My IA - RN-602 has many connectivity options  never disappointed me. It easily crank my Q Acoustic speakers 3090i. Now many advanced models introduced from past one year like RN-803 

The marantz pm8006 is an outstanding integrated amplifier. Fantastic upgraded phono stage, incredibly powerful sounding, yet refined and able to do subtlety. It has more connection options that I’ve seen on any other amp. Just keep in mind that it is fully analog. You can always pair the pm8006 with the also top notch na8006 cd/streamer. $1199 for each, but Amazon has them discounted now and then. I own both the pm8006 and the PM14s1 integrated and I’m telling you they are very close. Although the pm8006 is the more neutral, whereas the 14 has a warmer sound. Funny that not many recommend the marantz products often here...sorry to see as they are missing out on very good sound and very good value. This of course is coming from a Marantz guy😁
However in looking at your post I did just now notice your budget....and the fact you need streaming etc...(although it Is my belief full analog amps sound better) you could grab the marantz pm7005 which should take care of all your needs imo...

Onkyo A-9150

A budget amp with a good 3D soundstage and decent dac.

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.