I too like EL84 and 6L6 tubes. The KT66 is pretty similar in sound to the 6L6. The EL84 must be an easy tube for builders to work with (probably allows for use of cheaper output transformers) because that is where you most often see it being used, but, I like the lively and punchy sound that tube delivers without being harsh. The 6L6/KT66 are terrific sounding tubes--rich, yet plenty of clarity and good amps running those tubes sound "big" (enveloping soundstage and sense of weight and scale).
Of the small triode tubes, I like 2a3 and 45 the most. But, of course they do have limited output and cannot be used everywhere.
I don't know about the tubes that are used in the output transformerless (OTL) amps I've heard and liked. Unfortunately, there aren't that many makers of this type of amp because many tend to be unreliable. That left Atmasphere, a very reliable brand, to this field. The Berning amps (including the Linear Tube Audio) are sort of variants of the OTL (they are interesting, but for my taste, they are not voiced the way I like tube amps). Anyone interested in tubes MUST, at some point hear an OTL amp--for some it is like a religious experience--the dynamics and liveliness can be shocking.
With tube amps, more so than solid state, you really have to hear what you are considering for purchase because of the wide range of sound. While I am a tube electronics person, I find that there are plenty of tube amps that I would not want and I would get a solid state amp instead. This is particularly the case with high-powered tube amps. If I really need that much juice (I don't because I don't listen at high volume in a large room), I would consider solid state instead.