Tube amps - what 3 things…

The most important features depend largely on the buyers attitude and expectations regarding components.  If you are someone who is bothered by having to maintain/fix gear, or are bothered by the fact that tubes start to go bad from the moment they are turned on, then tubes are not for you.  To the extent you have some tolerance for the nature of tube gear, but, you are still concerned about tubes wearing out, that might affect the kind of gear you should buy.  The type of tube chosen, and how hard the particular amp drives those tubes, are BIG determinants of how long tubes will last.  There are amps that will run for many decades without the tubes having to be changed, others might need new tubes every couple of years (or earlier).   Tube amps tend to be more noisy than solid state--hiss or hum or intermittent crackling, etc.--you need to factor in your personal tolerance in deciding what to buy because some otherwise great sounding gear might be prone to be noisy.

For all kinds of gear, not just tube amps, decide what features are necessary.  To me, remote control of volume and some form of balance control is essential.  Given the nature of tube gear, I would think that small channel imbalances are inevitable and the ability to compensate with a balance control is a must.

The world of tube sound is vast and very variable--much more so than the sound of good solid state.  You need to listen to enough gear to determine what fits your ear.  Personally, I don't think there is only one type of tube topology (e.g., single-ended triode) that is clearly superior to another, but, there are some listeners that have a clear preference.  I have heard versions of pushpull pentode/tetrode amps, single-ended triode and output transformerless amps that sound terrific, often in quite different ways.  I think the type of tube, and the brand of tubes matter too, but again, these are personal preferences so the only recommendation is to hear plenty of different examples to develop your own idea of what to buy.  Finding a friend and/or a friendly dealer that can help you sort out options would be a big help.  If you attend a big audio show, you can also taste different gear or find people that can help you make the right choice.

what speakers?

different tube amp qualities and features matter if you are driving hyper efficient altec horns or audio notes, less efficient harbeth monitors, reactive focals or revels, or resisitive magnepans

just like ss amps, they should be optimized to the speaker load and power/current demands

right?

What speakers. A VERY important consideration. Auto bias, tube rolling ability, quiet design

Quality transformers are a key part. That's why I like Quicksilver.

https://www.bandwidthaudio.com/post/output-transformers-the-heart-of-a-tube-amp

You didn’t mention Tube Preamp, which I think is more important regarding features and system sound

1. my Cayin A88T Integrated Amp, Bias Controls

I wish it had exterior bias meter and controls. Someone else mentioned auto-bias, that would be even nicer. Unfortunately I need version 1 as it is the only one with 16 ohm taps, and it’s bias adjusters are inside, take bottom off, better avoid touching ...... Great review made me pick it, but I wasn’t paying attention to bias controls.

Preamp Features: My McIntosh mx110z is a full featured Tube Tuner/Preamp, up to spec by Audio Classics, especially new gold rca jacks. I started with Receivers, then separates, then no controls, now back to full features, integral phono and tape .... Vintage McIntosh units have their MODE switch, which is very helpful for me to match my speakers side to side when messing with level controls, stereo reverse, l to, r to mono .... Not everyone needs the Mode control, but I do.

2. IF I went for an Integrated Amp, with remote features, I would definitely want at least remote balance as well as remote volume. My Cayin is an integrated amp, but I only went for that to get remote volume so I could stick with my Vintage Preamp. I only use 1 input, and I think remote control inputs is dumb.

There are many errant tracks that benefit a LOT from a small tweak of balance, especially compilation cds/lps/tapes. A lot of recorded live performances, the 1st track, eh, not quite right, the room with people in it is different than the pre-concert set-up. the engineer figures it out, makes slight corrections for the rest of the recording,

3. IF I didn’t have level controls on my speakers, then I would like to have enough tone controls (not a full equalizer, but several bands, not just treble/bass).

That’s hard to find on modern equipment. I just don’t believe in buying a great speaker and expecting it to sound great in .... unknown room. Much room treatment results from the lack of level controls/decent tone controls that can be refined using a sound pressure meter (quite affordable these days).