"SPECS, ATTRIBUTES OR CHARACTERISTICS OF AN INTEGRATED AMP TO CONSIDER"

If you're looking for an integrated with the ability to drive many speakers, a capable on-board dac and streaming, you might take a look at Hegel H390 or H590.

... matching it with speakers used in their system...

@joscow 

Your speaker's sensitivity spec should give you an idea of the minimum amount of amplification you need to power your speakers.  Also, check out what the manufacturer recommends.  See what amplification others are using with your specific speaker brand/model by researching and asking on forums.

How it sounds isn’t a spec, but is always a major consideration IMO. It’s always best if you can try it in your system. What speakers are you going to be driving?

The power supply and current flow are significant factors in the amps ability to drive more difficult loads, so compare the 8 and 4 ohm power ratings....a true doubling of power into 4 ohms relative to 8 ohms is a good indicator.

The quality and features of the phono stage can also be a big consideration when comparing one unit to another. Options for MC and MM can be useful, as is the ability to select different cart loads.

Is a remote something you’re interested in?

I’m distilling down this complex question into three main factors IMO.

(1) The upstream electronics display their own bespoke sonic signatures, just like speakers and the rest of your system components. Simply put, your ready-to-audition list of amps may or may not provide that ethereal system synergy with the rest of your system. Personal auditions strongly suggested over the hyperbole in published measurements and graphs and blind recommendations.
Choose wisely.

(2) I’ve witnessed numerous disappointing failures wherein fans fall into the illusionary trap of thinking expensive speakers will cure all the performance warts, shortcomings, and performance compromises inherent in comparatively cheap amps and sources .

the amps & speakers philosophy is clear. An affordable speaker with good amplification (and source) makes more sense than an expensive speaker with a cheap amp and source.

(3) Amplifier design, power ratings, & robust power supplies

If your speakers are demanding to drive you’ll need a suitably muscular and beefy amplifier and power supply to support them.

(A) Simple power output guideline with a qualifier below: Don’t look only at the headline power figure - see what happens when the impedance drops to four ohms. If the number nearly doubles, then your amplifier has good current delivery and will be capable of driving more demanding speakers.

(B) BUT ….and its a significant “but”,.. it doesn’t have to be a full hard yes or no choice adherance choice for above- noted full “ doubling”, if the amp build and design is a no compromise,super high performance, dual-mono design amp.

The biggest difference between dual-mono and simple single stereo feed is the power supply and grounding.

- A dual-mono has completely independent power supplies, power grounds, and input grounds. It’s basically two completely separate mono power amplifiers that will easily excel and drive the most demanding speakers.

- A stereo power amp usually shares a common chassis , power supply, and signal ground.
 

The biggest advantage to going dual-mono is the availability of each power supply to power each channel with maximum independent channel shielding and robust power. A simple common stereo power supply can be taxed when large, low frequency transiants are present on both channels.

Don't forget that the ultimate performance of your system will be limited by the room itself.  Budget for room acoustics early on.  This can make modest systems sound much bigger and more powerful and get you off the carousel ride of equipment swapping early.