[Elizabeth]

Rock by either band name as presented,  or artist last name.
Jazz same.
Classical by Composer, then size of work. Sonata, duos trios quartets, etc. up to symphonies, with all vocal last, Masses, Opera.
Within each group the artist in sonatas, group once up to trios and quartets, conductors for concertos Though for concertos often by star player within that composer Concertos for * instrument instead so messy? (I list instruments alpha so clarinet, French horn, piano violin  symphonies by conductor then numerical order
Then on key part is all by composer then size of group. So at least some order.
For multiple composers on same LP. I just bought it for one usually.
Then there are a few items that are many various composers, like Horowitz playing etc. so the go under Horowitz as if by composer. sucks but all I got.

[Scroof Neachy]

I don’t organize my vinyl in any particular order. I’ll have the Beatles next to Quicksilver’s Messenger Service and Perry Como beside MC5. It’s completely random. That way it’s always a surprise when I reach for a record. If I grab the first one, I put it back somewhere else in the collection. It’s like pin the tail on the donkey - sort of.

[rockadanny]

Mostly by last name. However, many aliases, such as Muddy Waters, I list under "M". And for band names, such as The Beatles, I list under "B", as in, "Beatles, The".
For classical, I try to order those as composer last name. However, sometimes I'll list under the performer's name, especially if I have multiple releases from them, such as "Bartoli, Celia".
Frankly, I guess its messed up, but makes sense for me when searching.

[marvda1]

i overheard at half price books artists by last name and groups by first name.

[S Clark]

It's all pretty easy except classical.  Jazz is by artist.  Art Blakey and the Jazz Messengers is under B.  Except for the early years where Horace Silver was co-leader, then they are under J for Jazz Messengers. Or the Manhattan Jazz Quintet, which doesn't have a leader per se- under M. 
It's classical that's a bitch.  I group first by genre (sometimes difficult)... Medieval, Baroque, Classical, Romantic, 20th Century (so is Rachmaninoff Romantic or 20th Century?).  If a pianist is playing stuff from all over the repertiore then it goes by artist in a misc. stack (unless one track is the clearly primary track).  Then there's Indian, then there's anthropological, then there's odd box sets, and then......
No matter how organized, there's always something that defies classification.   

[Digi-G]

Also, there's groups like 'Til Tuesday.  I always remove the ' symbol because I don't want them at the top (or bottom) of my list; I want them grouped with the T's.

Plus, I want my filenames to reflect what I see when I play music.  Windows/Microsoft doesn't like special characters like that.

[Early B.]

In my last move a little over a year ago I threw out all alphabetical classifications.  I put the selections I like best on top shelves and worked my way down to least favorite on the bottom shelves.

This. I start with my favorites/reference material on the top shelf and work my way down while grouping each artist accordingly. If you make it to the top shelf, you're one helluva talented artist and deserve plenty of playtime. I also have three batches of CDs in separate locations -- the good stuff, the rarely do I listen to stuff, and the never gonna listen to again stuff. For my digital files, it's organized by first name.

[Vincent Kars]

So who is right?  Me or my ignorant slut of a friend?

Your friend 

In general the internet databases we use for tagging our music collection will almost invariably return "First Last"
Under the hood there might by tags like SortArtist containing "Last, First" but often this is generated by the media player.

[sebrof]

So who is right?  Me or my ignorant slut of a friend?

Both
Neither

[viggen]

most of the time the artist's name is also the band name so keep it the way the artist prefers his/her "band" name to be read.

what irks me is when the band's name starts with "the".

[Craig B]

Obviously, people can (and do) file in any manner they want. As long as their system works for them, they've got a working system, and that's all that matters. But it doesn't mean their system is "right" in the sense that it conforms with objective professional organizational standards, because it doesn't, and only someone who never learned how to use a library would say that it does.

As far as preceding articles go, like "a" and "the," these same filing systems have long agreed that those kinds of words are disregarded when filing, so there's no reason to be irked by them, any more than there's reason to be irked by band names one might normally expect to have a preceding article, but whose members insist they don't, like Foo Fighters and Eagles (though I don't think the latter have pushed the point in quite a few years).