Tube amps - what 3 things…

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).

My advice is to download the Decibel X-pro audio app for your smartphone So you can get a rough idea of how loud you like to listen. This will make a big difference. I used to think that high power was required then I got speakers that were 93dB efficient And started listening to 7 and a 1/2 W. And I loved the sound then I went down to one and a 1/2 W and love it even more. But I’m listening right around 70 to 75DB and fairly close to my speakers. This wouldn’t work for a lot of people.

 By the way, I think you're getting a lot of good advice on this thread actually. Ultimately you gotta think of things in terms of a system. And the speakers in the room and the amount of stuff you have in the room is part of that system. Donnie Darko (?) has a good YouTube video about room treatment that's worth checking out. 

I see recommendations for autobias.  I much prefer manual bias. I Like to be able to calculate my preferred bias and adjust it.  For example sometimes i run tubes that have a max voltage near my b+, so I'll lower the current a bit and run at a slightly lower plate dissipation power.  Additionally manual bias will tell you if one is biasing much differently than the others, meaning a degraded tube.  

If all this seems like work to you, then go with auto bias.

Jerry

Tube amps tend to be more noisy than solid state

Not if they are properly designed and installed.

The world of tube sound is vast and very variable--much more so than the sound of good solid state.

Not true. Tube amplifiers are current devices. Many hook up tube amps to roller coaster, Mt Everest peaky impedance speakers. Not the best match. Solid state is  just as variable. A lot of it comes off a production line and is improperly set up. 

Tube gear has a magic that solid state doesn't. If you're a bottlehead, you're hooked for life.

Tube rolling is a fools errand. Tubes are not identical, not even matched sets. Rolling various tubes in and out without any idea of the tube condition and how far it varies from design center is silly. VERY few tube rollers measure and balance different sets and what they hear are level and distortion changes. See ieLogical Rolling

Autobias is nice and generally works very well. However a catastrophic tube failure can take out the AB unless there is other monitoring to shut down the amp. Today, I wouldn't have an amp without it. Most AB circuits allow you to select a preferred bias. It requires a trimmer and a voltmeter and a healthy appreciation for sticking your hands in and around several hundred volts DC. MESSING ABOUT IN A TUBE CAN KILL YOU IF YOU ARE CARELESS.

Nobody has mentioned the driver stage. Some amps have CCS for phase splitter AC balance. Others have fixed resistors that are calculated with an ideal tube, but are seldom exact. Others have a pot for adjusting AC balance. This is the most flexible BUT requires test gear for optimum - read lowest distortion - results.