There's a pretty good community on Reddit, /r/patientgamers, that is all about visiting past gaming titles. It's probably a good idea to read a bit of their opinions before delving into a new game, you can find little tips and whether the game has actually aged well there. (Contemporary reviews can't tell that.)

The Secret of Monkey Island (c. 8-16 hours, idk lmao)

It's a pretty rare game in that it's genuinely humorous and is honestly really sweet. Guybrush Threepwood is just a boy who wants to be a pirate! And the game universe takes this seriously enough to set a tone that this is indeed a legitimate pursuit. It's pretty close to the ideal introduction to the adventure genre. If you hate it, you probably won't like the rest of them either. Some points in favor:

1. There's a remastered edition that works on modern systems that lets you also choose old presentation. Secondly there's a great software that lets you play these old adventure games named ScummVM. You can actually play these on modern systems with minimal hassle!
2. The first act is like a god tier tutorial into how the game systems work. Thus the real game gets to begin straight on and you don't need to consult shit like manuals and maps that were the norm for, say, really old school RPGs.
3. It was so influential on graphic adventure games that if you enjoy it you can find plenty of similar titles.
4. The biggest problem of adventure gaming, poor puzzle design, is mostly absent here. The creator wrote an essay on the topic and it shows.

EarthBound (c. 20 hours)

This game has sort of a weird reputation. There's too much emphasis on how bizarre and odd the game is in lieu of conveying what the point even is. On one level, it's one Japanese man's take on Americana and the way America sees the rest of the world. On others it's a game that is quite cognizant that it's a game (it's like anti-immersion), it's a growing up story, a road trip. It's pretty cool in how it uses game mechanics to convey characterization. It's sort of a mash up between science fiction and magical realism. I feel it's general viewpoint is like genuinely good and valuable. Some points:

1. If you're aware of the general RPG mechanics, you get many of the meta aspects. No need to play other 8bit or 16bit RPGs before hand. It's imo the best 8 or 16 bit rpg so it makes a good enough introduction to them.
2. The soundtrack is real solid and the graphics are solid among 16bit rpgs - I think people mistaked the art style for laziness, but it's clearly quite deliberate.
3. One of the most famous boss fights in all of games.
4. I honestly prefer the Blues Brothers parody to the original thing. They are a joy! The references the game does aren't just Family Guyesque jokes, there's some amount of respect for source material at play.
5. It's not a difficult game and the battle system isn't very central. Which is good, because I don't think RPG battle systems are that interesting really. There's hardly any grinding in the game save for the first town.
6. It was created by a non-gamer and honestly it shows positively.
7. There's a good sequel Mother 3, if you like the game and want more Shigesato Itoi goodness. Actually Mother 1 is pretty good too.

Nethack

This is perhaps the most dubious choice on this list. If someone knows a clearly superior roguelike, that's probably the thing to choose instead. You should totally read a whole lot of spoilers, it's how everyone plays the game.

Honorable yet possibly dubious mentions:

1. The Incredible Machine was a great puzzle game back in the day. The task is to construct Rube Goldberg contraptions.
2. Some GTA game. I've never finished any of these, but have played lots of four of them. Just driving around and doing random shit was fun enough on its own.
3. One Civilization-like game is totally worth a try. My favorite is Sid Meier's Alpha Centauri. It's one of those titles where the whole is better than the sum of its parts. After a planetfall, competing ideologies group into factions and duke it out for survival on a hostile planet. Curiously there's also a plot to this game that plays out to completion if you manage to transcend to the next level of being, that is, the technology victory. Also a shout out to when game covers were cool: 1, 2
4. Canabalt. An infinite runner web game that was incredible back in 2009. It's a good example how simple a good game can be yet use setting, audio and graphics to great effect. You can sense the hopelessness and desperation (and feel these yourself) as you play the game, but the game has no lore (thank god).

What I should try out

Fallout 1 and Fallout 2 are the biggest gaming omissions that I probably should get around to play. I watched a hbomberguy video dunking on Fallout 3 and the man came hard in favor of the earlier titles.

Xcoms and Jagged Alliance 2.

Rocket League is a lot of fun.