You need to think first about tube vs solid state… although some solid state, like the Pass XA series are very warm and tube like and visa versa Rogue.
Brands you should consider first and foremost are Pass (solid state) and Audio Research (tubed). Others, solid state: MacIntosh (tubed or solid state, heavy with midrange and bass… light on detail, look cool), Luxman (heavy on treble and bass… so detailed ( shy on midrange a consequently not musical), Krell (warm) Tubed: Conrad Johnson, VAC, Cary (really warm and musical).
Obviously there are others. Also lower tier NAD and Rotel.
I would read a lot and audition a couple key brands. They have house sounds… so in general they have the same kind of sound with gradual improvements over time… so listening to a current MacIntosh and Pass will give you a good idea of what you are in for with the brand.
Nice amp character summary, I am saving it for future reference! Possibly worthy of it’s own thread.