If you are thinking of upgrading your speakers the advice of upgrading those first, prior to the integrated is really good advice. Synergy as noted in several responses is so important between gear, especially speakers and amp. It’s tempting if you are going with an Integrated to get an Integrated with everything, DAC, Phono Stage, Headphone Amp, the list goes on. Really good advice I got from others is to focus on what sounds best in an integrated, getting the best pre / amp combo. The Phono Stage, DAC are items you can add into the mix and you’re likely to get better performance and flexibility by going that route. If you have your heart set on an Integrated, one box that has everything and does it all well, the NAD mentioned in this thread is an unbelievable value, great performer. The streamer / DAC built in is extremely well done, has room correction, really does it all and is about as future proof as you could hope for.
Integrated Amps I’d add to your list:
Parasound HINT 6 - incredible value, bang for the buck, SS and can drive almost any speaker
Coda CSiB - Coda is probably the most underrated high end Hifi manufacture out there. The engineering, parts used and overall build quality are second to none, it’s not cheap but you’ll pay many multiples above there gear just to match it, it’s a no frills integrated, can drive pretty much any speaker.
Krell 300i - might be the most magical Integrated I have heard, something about the combo of power, control but also a liquidity, tubelike quality without any of the draw backs of tubes.
PrimaLuna Evo400 - All Tube Integrated built like a tank, no frills.
Linear Tube Audio - several Integrated Amps - like Coda, incredible build quality for the price with top notch engineering, if you want Tubes, really hard to beat and incredible value relative but not cheap.
McIntosh is a polarizing brand but they make solid state, hybrid and Tube Integrated Amps, hold their value like no other brand.
Hifi Rose RA180 integrated - highly reviewed, very well done Class AD amp, will drive almost any speaker
Niam - make several integrated amps that would cover all your bases, well thought out DAC/Streamer built in
Hegel - 3 different models, often one of the most highly recommended by those who own one. Very well done streamer/DAC combos, if you add a separate streamer / DAC can raise the performance which is already really, really good.
I’d buy used, buying Hifi gear is like buying a car, it depreciates 30-60 % as soon as you open the box, you can really stretch your dollar going used. Good Luck