First off, movies are indeed the worst way to experience anime. The style is primarily focused on series. I would consider picking a short series (6 eps or 8) and binge it.
The recommendations you’ve gotten so far seem to cater to you. They are movie lovers’ anime movies. Satoshi Kon is genuinely good cinema. I’m not sure it will “teach” you much about anime tropes and conventions though. You couldn’t watch those and claim to be an anime veteran/lover. I’m not really sure what your goals are so I’m not sure what exactly to recommend. If you’re looking to see what it’s like to be an otaku and hang out with anime fans, then that’s one thing. If you’re looking for good cinema, that’s another. If you want to know what life’s like in present-day Japan (or the closest approximation anime can provide), that’s another.
But, just to list some movies, let’s see what the internet says:
MAL tends to prefer newer things, so of course Your Name and Koe no Katachi are near the top of the list. MAL also prefers movies based on series somewhat due to series fans, so there are a lot of series-based movies there.
#1 is Your Name which is supposedly actually really good. Not just “new” good. So it’s on the list, except it hasn’t been officially released.
#2 and #3 are there because MAL probably. But if anyone has seen Koe no Katachi, please let us know how it is.
#4 is Spirited Away, which is fantastic and I’m sure you’ve seen it.
#5 is Wolf Children. That’s a great choice.
Skipping Ghibli and series-based movies, we end up at…
#15 Hotarubi no Mori e (Into the Forest of Fireflies’ Light), which I haven’t seen. It’s only 45 minutes though.
#18 is Bakemono no Ko or The Boy and the Beast. I’ve heard really great things about this one.
#19 is Grave of the Fireflies, which is very good.
Pushing all the way to 30, there aren’t any more that aren’t Ghibli or series-based.
But #33 is The Girl Who Leapt Through Time, which is fantastic.
Here’s my real recommendation though. If you want to “get into” anime, I’d recommend biting the bullet and watching a short series. My choice for that would be One Punch Man. It’s 12 episodes, so if you cut out intro and outro, it’s only about 4 hours total of stuff to watch. It’s very easy to watch, not terribly full of tropes, and avoids the common problem for 80% of anime, which is that it has to take place around high school kids. But it’s still a great introduction and is very easy to watch. It’s uproariously funny and not complex.
The only thing you’ll miss is that it plays with tropes and conventions a lot. It’s a takedown of shonen anime to some extent, and you’ll probably never pick up that thread.
Short series recommendations are the following:
Time of Eve (6 eps)
Rurouni Kenshin: Trust and Betrayal (4 eps)
If you want to be confused the whole time, then watch FLCL (6 eps)
If you have a Plex client, then I have most of this stuff on my Plex server. You should be able to stream it fine from my server, I rarely test it out remotely though and you sometimes need to tweak the client settings to get certain things to play correctly (i.e. 10-bit HEVC anime, of which I have some).
Editing finished.