I have been playing trombone for over 25 years in a complete mix of types of groups (orchestra, concert band, big band, musical theatre, brass bands, etc) and the most common mute I have come across by a long way is the straight mute. I have also used the cup mute and occasionally the plunger mute (I generally use only the cup/straight all in one in rehearsals), but they are the only mutes I have ever actually come across and needed. I do also own a practice mute though.
Thanks for this the Solo Tone mute is my favourite, as someone who plays a lot of 1930s 1940s music i always wondered how they got some of the tones in the brass instruments the Solo Tone is one i hear a lot of in late 30s and 40s music especially in Glen Millers arrangements its certainly a sound you associate with ww2 and of that time period, sounds lovely when you have several trombones playing.
You omitted the pixie mute which when combined with a plunger can almost make the trombone speak.................as I've heard you do with the Echoes of Ellington band many years ago....................................................