Sonic qualities of SET output tubes?

Blindjim- I found the same exact thing as Grannyring when I was using SETs (no surprise, one was the same exact amp, and neither of us has ultra-high eff speakers):

The music was wonderful at lower volumes, and they did drive my
speakers to go very " loud " I was initially impressed, only to find the sound not to my overall liking longer term.

It was this whole issue of sounding "loud" when a system should not sound loud when turned up. Rather, the performance should simply swell and grow with greater impact etc....

My mistake was not the particular SET amp, but pairing the amp with a 4-8 ohm speakers with sensitivities ranging from 89-93db.  My 8-20 watt SET amps, while playing these speakers loud, always fell a little short of greatness. 

I have zero and I mean zero technical knowledge but everything that Atmasphere has posted has turned out to be true in my experience.  If you do not want to be confined to ultra-high efficiency speakers I think this means you can rule out the 2A3 and 45 amps.  If you want to go SET, you will probably want something 6C33C, 211 or 845 amps with a moderately high eff speaker (95--96 dB).  I found that 300b and EL-34 SETs did not cut it in my 14 x 23 x 8.5' room, driving 95-96 dB speakers, listening mostly to the same type of music as you do.  Great sound at low-moderate volume, but when you get grooving and want to go a little bit louder, the sound starts to get less enjoyable and fatiguing.  OTOH, my 300b push pull that makes 27 wpc (VAC Ren 30/30) or my 6AS7G OTL that makes 30 wpc (Atma S-30) sound fantastic. 

I think it should be obvious by now that if your speaker or your amp selection is priority one, then you have to get a "matching" amp or speaker.  If you go moderate efficiency, or 4 ohm on the speaker, you are going to want a reasonably large, SS amp, of which there are many.  OTOH, if you decide first on a 45 SET, you are going to be restricted to a fairly small group of very high eff speakers (>100 dB/w/m).  Those are the two extremes.  If a tube amp is your first criterion, and you don't want to be restricted to the v high eff speakers, IMO, you will want something in the 25-30 wpc range (or greater) paired with moderately high eff, 8-16 ohm speakers.  To get that, you can go OTL or you can go push-pull.  The very high output transmitter tube SETs are, I believe, out of your (very generous) budget. 

To get back to your original question, I am persuaded by my limited experience and the technical explanations of others, that the differences between the "voice" of different output tubes is outweighed by the requirements of your amp/speaker combo.  Particularly with SETs, the power requirements dictate the tube choice.  As you go to push-pull or OTL designs, you have more flexibility in terms of both output tube and speaker efficiency.  Both Berning/LTA and Atma-sphere offer a range of power output options in OTL designs and some variation in tube types.  Push-pull designs offer the widest range in tube types and power output, giving you the widest range of tube-friendly speakers to choose from. 

@grannyring- I forgot about the 300b monos. 
@blindjim  - Grannyring and I went the same route; from 8-9 wpc 300b to 12 wpc EL-34 SETs with the same results.  My speakers were quite a bit more efficient than his (92-95 dB/w/m, 8 ohm nominal, flat impedence) but we both found that Atmasphere was right; when you are down in 10 wpc range, you need +/- 100 dB speakers and/or high impedance speakers if you want more than moderate volume levels in a mid size room.  I know Charlesldad (and others) have had great luck w 300b SETs driving somewhat lower eff speakers, but IIRC, his speakers are 16 ohm. 

Of course, you COULD opt for the WAVAC HE-133 150 wpc SETs @ $77K.  That would maximize your choices for speakers, if in fact you had any $ left over to buy speakers ;-)

Great list from Charles1dad, to which I would add
Classic Audio
Audiokinesis

Also Ref 3A are not true high eff but are definitely tube friendly due to part to minimalist crossover. 

Also note that not all horn-loaded speakers look like the Avant Garde horns. 

A couple of other thoughts:
Another way to skin this cat in terms of using moderate power tube amps is the way I am going at the moment...Atma S-30 driving quasi-full range Feastrex field coils above 60 hz.  NHT X-1 Active crossover  250 wpc Class D ss amp driving 2, 10" woofers per channel.  These are DIY open baffle speakers bought from an A'goner in CA.  You reduce the power demands on the tube amp by not requiring it to reproduce deep bass. If you've ever had an amp w power meters, you can watch them swing in time w the bass line. A somewhat simpler way would be to use monitors or single drivers and a pair of powered sub-woofers with built-in crossovers. 

As far as finding desired products in close proximity and/or being able to buy a "turn-key" system at a good price, I'll repeat what I mentioned above...go to one of the good high-end shows.  Despite all of the known problems of auditioning there, you will NEVER be able to hear as wide a range of speaker/amplifier combos at one time as you can at, for example, RMAF or T.H.E Show.  Never been to Capitol or Newport, but they seem to be similar.  If you hear a combo that floats your boat, you can probably cut a good deal on the show demos. 

horns and triodes are quite capable of bringing home the bacon!

Amen to that!  I've heard the M-60s driving the Classic Audio horns in a very large room at RMAF.  They R-O-C-K!!!