Pipeline:
I the everything BIAB package so I have all existing styles and my style count is 9,451
I ported those over into Excel and sorted by Genre and Group.
Of these, there are only 3 groups listed, Country, Jazz and Pop but those also contain many multiple sub-styles, Groups would not be a good choice to randomly choose from as that would not take into consideration the many sub-styles available.
After sorting the list by Genre, I see the following choices:
Ballads, Bluegrass, Blues, Celtic, Classical, Country, Disco, Doo Wop, Folk, Funk, Heavy Rock, Hip Hop, Jazz, Latin, Lite Pop, Medium Rock, Modern Pop, Pop, R&B, Reggae, Soul, Synth Pop and World.
Those have multiple choices thus there is a large grouping of random styles to choose from.
There are a few other Genre's but the choices are very low and I would not consider them worth doing a random choosing.
My opinion would be to use the following as random choice groups in the Random Style Picker. And those choices would be in a drop down list.
Ballads
Bluegrass
Blues
Celtic
Classical
Country
Disco
Doo Wop
Folk
Funk
Heavy Rock
Hip Hop
Jazz
Latin
Lite Pop
Medium Rock
Modern Pop
Pop
R&B
Reggae
Soul
Synth Pop
World