I have about 3,000 LPs (and around 6,000 CDs). I don't have the LPs cataloged, never felt the need, altho Music Collector or Discogs are both workable, depending. The LPs are stored in modular fashion in U-Haul Small Moving Boxes, which at 12 5/8" x 12 5/8" x 16 3/8" are sized precisely to hold LPs, are inexpensive, and are readily available. These boxes are laid top open on their side with the album jacket's spine exposed on simple plywood and concrete block shelves (in the ground floor storage room, thank you...) which keeps the LPs comfortably accessible yet stored correctly. (Remember that those LPs add up to *a lot* or weight when choosing where to shelve them...) The collection is sorted first by general genre: classical, folk, rock/pop, world, etc. Within a genre, the sorting is more ad hoc based on composer, performer, instrumentation or whatever seems most salient about an LP. If one uses software to catalog one's LP collection, the sensible way to file them would be to match however the software sorts them.
CDs are a different matter...
CDs are a different matter...