I wouldn’t say that I classify my collection solely by genre, although I do use Genre tags. For albums or DJ mixes that envelope multiple genres I use multiple tags with a delimiter. Ex. Hip Hop; Shoegaze; Alternative; Rock
As for the directory or folder structure, it’s Artist - Album.
The music server application that I primarily use, Logitech Media Server, offers full text indexed search. That is, every tag, including embedded lyrics and custom ones, are available for query in its client applications.
Mp3tag. I’ve tried a couple of others, but kept coming back to it.