I planned on answering this when you first posted it, Ken, but I wanted to make sure I had enough time to complete my post, seeing it's going to cover many a year.
When I first started collecting 45s in the mid 50s, I bought a carrier box. This was a small metal box that held up to 75 45s with numbered dividers between each record, little sticky numbers (1-75) that you could stick on the record labels, and an index sheet on which you could list the records, artists, label and sticky number. So the records I put in there were basically listed in the order I bought them. So that would be more-or-less chronologically. When it was full, I bought another case. But by then, they were making them out of a heavy cardboard stock, and they only held 50 records. Then later they had other cardboard carriers that were double-sized and held 100 45s each. I also bought about 2 or 3 of those. So in the early years, my records were more or less chronological, and kept in those boxes. After a while I stopped buying boxes, and as I acquired more records, they'd just be kept loose. During my high school and college years (I was still living at home during college) my dad (who was extremely good at carpentry) built me two bookcases. The bottom shelf on each bookcase was built high enough that I could put my LPs in there, standing up.
When I left home for grad school (U Maine) in 1966, I had only a few hundred 45s and maybe 40-50 albums, most of those classical and show tunes.
I think I've posted elsewhere about finding a jukebox store not far from where I lived in Bangor, that sold the 45s after they were removed from the jukebox for 25 cents each. My collection grew tremendously after that. I just kept my records in cardboard boxes, alphabetically by artist. But I'd play them so much, that they were usually out of the boxes (at least I had the brains to put them back in their sleeves), piled up and mounded all over the place.
The one thing I started to do while I was up in Maine, was start a card catalog of all my songs. I say songs, because I kept the card catalog alphabetically by song title. (The 45s themselves, when they WERE filed, were by artist, so it worked out as a kind of cross reference.) The catalog, on 3 x 5 cards, were kept in several old metal file boxes that I picked up at a couple of garage sales. Each card listed "A" side song title, Artist, "B" side title, label, record number, and year. If the "B" sides were hits, they would each get an additional card. I also included cards with hit tracks from my albums (the album title would go in the spot reserved for the "B" side of 45s.) and all tracks from the several album compilations of various artists that I had picked up. To this day, the card catalog is complete and in order for all my 45s and pop/rock album hit tracks - vinyl only.
The albums themselves were (and still are) stored on those bottom two shelves of the bookcases and on shelves of an entertainment center that I bought in the late '70s. The albums are categorized as: Pop/rock music-single artist, pop/rock music-various artists, showtunes, comedy, and classical music. Pop/rock music single-artist are alphabetical by artist and chronological within each artist. Pop/rock various artist collections are alphabetical by record label and chronological (to whatever degree I can) within each label. Showtunes are alphabetical by title; comedy is alphabetical by artist, and classical is alphabetical by composer and then broken down by type of music.
Back to the 45s. When Nancy and I first got married in '76, I bought a five-drawer legal sized, lateral filing cabinet (bought it used, got it cheap). legal size means that the drawers are 14 inches wide - ideal for storing two parallel rows of 45s in each drawer, upright. So the 45s went in there, alphabetical by artist - and by title within each artist. I used the old partitions from my first 45s storage box to tab the beginning of each letter of the alphabet and some other key spots (like "Be", "Pr", etc.) By the mid '80s, my collection was getting too big for the five drawer cabinet, and I bought another two-drawer legal size cabinet. My 45s remain to this day within those cabinets.
Never had enough 8 tracks to worry about (thank God), and don't have anything to play them on anyway.
I never bought any prerecorded cassette tapes, but in the pre-CD burner years, I made about 70 or so tape mixes, or direct copies off of vinyl albums to play in my car. I rarely if ever play them now, but I still have them lined up on a couple of shelves.
At this point I have about 150 or so CDs (haven't counted them). This includes some classical, some showtunes, but the majority pop/rock - most of them home made. - I remade most of my tape mixes onto CD for instance. My CDs are in a couple CD sized bookcases (I need to buy more - I don't like the idea of stacking CDs on their side, I'd rather keep them upright so I can read the spine labels.)
Even though my CDs are stored neatly, they are not ordered well. The classical and showtunes are separate, but the pop/rock stuff is in random order - except that my mix series (e.g., "No One Else Remembers vol 1-5", "Never made the Top 20" vols 1-5", "Play It Again vols 1-6", "Can't Get Them out Of My Head vol 1 - 11") are stored in order.
None of my cassettes or CDs are cataloged yet. I won't do the tapes because they are copies of vinyl, but I still plan to catalog the CDs. Someday
Finally, about 5 or 6 years ago I started to put my card catalog onto an electronic spreadsheet. That is a huge pain in the ass. I'm about up to the "M"s now, and work on it only once in a while. When I (if I) get to the end of the card catalog, then I'll add the CDs.