I have also started using the Discogs "Collection" feature to catalog my modest collection. The most time-consuming aspect is identifying the correct pressing from the "deadwax" markings. The Discogs feature allows you to write in your own comments about each record, which is quite useful. Using this feature will assist if you or your heirs ever want to sell any of your records.
Physically, I have an idiosyncratic way of organizing my LPs. They are more or less organized by genre, year of initial release and country of origin. One of the advantages of this is that if I pick a late '60s British-rock album to play, there are similar albums nearby that might constitute a good choice for the next to be played. You don't get this by simply alphabetizing the collection. I suppose one could use Discogs to achieve what my physical organization allows, but I wouldn't want to have to pull out my laptop every time I want to play a record.
I have an extraordinarily good memory, so that probably helps in using my physical-organization system. I remember what year many of my albums were released. If that is unimportant to you, you could certainly try a variation of my system, perhaps just organizing by genre, country and then alphabetically (by artist) within each genre.

