How do you sort your LPs?

Just make it easier on yourself and not over think this and just do it alphabetical.

while you are at it....make a spread sheet of what you have also and can update as you add to the collection.

Alpha.
Genre is too hard as Eric says, too many artists fall into possible 2 or 3 genre's depending which way the wind blows.

I suppose it also would make a big difference according to the size of your collection and how often you add to it.

Genre, then alphabetical order

Remember the scene in Diner in which Daniel Stern's character reads his wife (played by the delicious Ellen Barkin) the riot act for mis-filing one of his LP's? She put it away in the incorrect genre. Great movie, great scene.

Alpha by artist.  If you want to catalog them, consider putting them into the Discogs database.  You can then download a CSV file from Discogs.