Great topic! I've been tube-amp curious for some time. My tube experiences have been limited to a Modwright preamp and a CDP. So far, I feel like I'm chasing a chicken but all I can see are feathers. No, I'm not a farmer, just like the expression.

While there are many tube amp fans and many of them are happy to report on their experiences on tubes and amps, these experiences are not easily transferrable from one system/listener and another.
From a great amount of reading and thinking on this, I can forward the following thoughts:
Tube amps and their tubes are tremendously variable in properties, far more than their SS bretheren;
Power ratings first are hugely variable - SET amps are available with as little as 1 watt of output power. The SET crowd seems to think the lower the power, the more magical the amp. Elitist dogma? "If your speakers can't "do" 1 watt, don't even grace this room with your breath, sir. Everyone knows your hugely overblown 300B amps can't create the magic of a 205D." [Rule 1]
Within the SET crowd, the camps are further divided. 845 tubes can produce 18 standard watts, which is huge for SET. These amps could be used with most conventional speakers, as long as they don't present a difficult load. 300B's, 2A3's, and 45's are the most common tubes used for SET amps and provide a standard 8, 3-4, and 2 watts respectively. The current wisdom is that 45's make the best SET amps, but chances you have speakers that will work with those are slim. 300B's are considered meatier and prototypically tubier, but possibly fuzzier and slower by comparison. 2A3's are considered "the best", depending on the listener, falling somewhere between the 45's and 300B's.
Push-pull amps have the advantage of power, as two circuits are used and tubes are doubled up. These have the reputation of bigger dynamics and superior bass, which makes sense with their added output power. Of course, SET-heads point to Rule 1 and add that the added complexity translates to reduced life in the midband. Some people prefer PP amps, as the added power and headroom remove some of the limitations that SETties live with.
There are a huge number of PP amps and tubes to choose from. 200-watt tube farms are available, though it makes me shudder to think of retubing these monstrosities, but if you like big, inefficient speakers and love the sound of tubes, this might be the way to go.
Of course, there are also OTL amps which combine the wonderful attributes of low power and many, many tubes. I know nothing of them and they are truly a sect within a cult wrapped in an enigma.
Ultimately, it seems every tube-amp story is different. It's far from a plug-and-play decision. Bill at Response Audio is lucky enough to actually hear a lot of this stuff. Most of us aren't.
Me? I have very efficient speakers and have ordered a Yamamoto Sound Craft A-08s; a 45-based SET amp. It should be here in a couple weeks.