How do you store and catalog your vinyl?

  Personally I hate Ikea Kallax shelves - yes they are cheap and no doubt this is why they are so popular.  IMO, the shelves are too deep, not high enough,too many records are in each compartment making it quite heavy and you have to put your own back onto the shelves.

  I have been lucky to have my own design shelves made by my Uncle - for me they are perfect - the 3/4 high dividers release the weight strain of too may records and also allow you to easily flick through records.
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my vinyl is sorted strictly A-Z except for Classical, Soundtracks and Various artists have their own small area.
  Discogs is used to catalogue my 95% of my collection.

@downunder, good point about the compartments in the Kallax being too wide, one reason I prefer the EKET. Each compartment in the EKET is 12-3/4" wide, still too much but acceptable. Owners of the Kallax have solved the problem of their excessive depth by installing a block inset into the back of each compartment. I also don’t like the Kallax’s open-back design, but a thin piece of plywood or melamine can be attached to the rear, closing it off.

My collection was about the size of yours when I started to organize it last year with Discogs. I got a couple of Kallax shelving units from IKEA and went to town. While organizing, I noticed two things: several records I thought I had I did not (lost in multiple moves, stolen, gotten rid of...) and I had a few records I had no idea how I got them. I quickly started culling and adding, all the while finally LISTENING to my records. Just hit 1500 this week, so beware. 

I organize first by a few categories ..... symphonies, chamber music, other orchestra, and then by composer within each group.  Then jazz, singer-songwriters, early rock, test/demo records, and misc other.  Within these I arrange alphabetically by performer.  I've got over 1200 lps, and 1100 cds, and the system works for me.

I do this because I usually choose what to listen to by category first, e.g. I fell like listening to Judy Collins tonight ... then it is easy to remember to go to singer-songwriters and find "Collins" group of discs.  Then make a choice.

A lot of great suggestions. 

On organization - here are 10 different methods to organize. I bet there is at least one way you've never thought of, and might like. I'm actually a fan of release year.

http://www.vinylmeplease.com/magazine/organizing-your-record-collection/

You sound like you are slow to jump into an app to organize. You have nothing in the world to lose trying out Discogs. Put in a couple of albums and see if you like it. There is a massive benefit to that system - the notes people have submitted are incredible. Honestly, given the love for details, I'm surprised more people didn't say Discogs as no other way to do this. 

In those Discogs listings are more details about each release than you can ever imagine. My personal favorite - runout / matrix listings. You can pretty much definitively determine which release you own. Honestly, dollar value is fun, but a lot less useful. 

And, if you are ever out buying records, you will never buy a duplicate.