Best way to organize 6000 albums?

Don't EVER bother to "organize"...leaves much more time for listening...anyway, new albums are arriving chez moi too quickly to even listen to ALL of them...y'know, 2 tracks and I don't like it so on with the next one.

More important to preserve the cover art and replace the liner with proper rice paper sleeves and the jacket with heavy vinyl dust covers.

Every organization I've tried has its pluses and minuses and takes time to maintain. I am currently using one like jwc37 which works especially well for classical except that I uses a palm handheld with handmark modiledb software rather than a cardfile. Also like pls1 I keep printed lists handy. The palm is great for the listening room, silent, instant on, simple to use with a lighted screen that makes updates when the room is dark easy. The software is not perfect, but its sorting, filtering, searching and data entry functions are pretty good. I keep entries organized by performer, composer, work, date, label, label number, media type and condition, and misc notes like personal rating, price, etc. For shelves check out www.storadisc.com/custom.htm at about $1 per LP.

I have a collection of about 2000 classical LP's. Finding a particular one was sometimes a difficult task. I undertake to catalogue them using CDpedia, a software that runs on Macintosh. There is also the mobile version (Pocketpedia) that display the database on an iPhone or iPad. You can do modifications of the database on both. CDpedia can also download data from a variety of sites. I use Discogs where I find 80% of the entries already documented (included the Artwork, the Label, the tracks, etc). Very satisfied after two years of use.

Before my last move I had about 13,000 LPs. Moving I cut that to 6,000 moved to new home. (the majority of the tossed were Classical) Since then I am down to 4,500 and am working on getting down to 3,000.
I have equally Rock, Jazz and Classical LPs.
Split into the three types. all spine out, by artist/band for Rock, Artist/ group for Jazz. And Classical by composer, with Sonata first, alpha Piano, violin etc. Then duo, trio quartet.. up to symphony, then opera, or vocal if any. Within each part, say Piano sonatas, I have them by artist playing ABC order. not individual piece order. Concertos, Symphonies ARE each one, then conductor name. (since I have a lot of each, particularly Beethoven)
For Rock and Jazz, I ’try’ to keep them in chronological order within each artist. This is hard to keep really perfect. but it DOES help me to learn which album was before another etc. More important in Rock and Jazz. Now and then I use a book to help reset the order if it is getting bad.
It would be nice to have a Jazz database mentioning who played in what group when.. plus those special one time groups for a new artist first recording etc. Rock is a little like this, bit not nearly as much.     
If I were filthy rich, I would HAVE duplicates so every Jazz artist of note would have all the albums they took part in in their section, in chronological order.     
A browsing section would allow both Worlds. Instead of the immense space needed for all flopping face type display, have a FEW sections at eye level set that way. all the rest spine out. Above and below. leave the most used/played LPs in the open area. the rest put away.

I had about 1500 LPs. Then my closest audiophile friend died and left more than 6000 LPs, from which his wife invited me to take my pick.  I selected about 900 of his LPs, and I think she gave away the rest.  Faced with that windfall, I found a furniture company in Brooklyn that would build me a custom cabinet to my specs, designed for about 800 LPs to be stored on end with the binders facing out.  I also bought a second cabinet that is more like the one you describe, covers facing forward so you can flip through them, two shelves with two rows per shelf.  That probably holds about 500 LPs.  I keep jazz vocals in that cabinet, arranged only by alphabetical order according to the names of the vocalists.  (On another level of my house, I have two more storage spaces for jazz vocalists.)  In the new 800-LP cabinet from Brooklyn, I have nearly all jazz instrumentalists, all arranged alphabetically by player names.  The lowest shelf contains some vintage R&R, including Beatles and Stones, and some Latin jazz.  I don't organize by label at all.  I go by the artist and the genre.