I suggest anything by Jeff Vogel; Exlle, the older Avernum games. This man's been in the business since the heyday of Shareware.

I would recommend a simple game, like the original Doom:
https://www.gog.com/game/the_ultimate_doom

If you liked it, you could move on to other FPS fare, like Shadow Warrior and Blood:
https://www.gog.com/game/shadow_warrior_complete (Free DOSBox version, so you could actually start with that instead)
https://www.gog.com/game/shadow_warrior_classic_redux (Remastered version)
https://www.gog.com/game/one_unit_whole_blood

I would also recommend Sanitarium as a point-and-click adventure. Despite having low resolution, it's very atmospheric, simple to play and does not have any particularly difficult puzzles.

This is a bit of an odd suggestion, but you might want to look at what games there were early on in GOG's time, possibly try restricting yourself to games released during the beta phase. The reason I suggest this is that as the true gems started running out, GOG started bringing in many of the more mediocre games of old. The ones available early on were what enabled GOG to break into the market, and thus could be argued to have had more appeal.

That said, it means the publishers that signed later such as LucasArts and EA would be ignored, and ignoring Grim Fandango would be criminal.

The other thing to filter by is a 5 star rating. It's not easy to be liked by everyone, so those games that do are probably worth a look. A combination of such filters on your search (not sure if GOG can apply these filters, but you can mentally) should help identify a few true classics.

Oh - and play Psychonauts immediately. And Sacrifice if you can get it to work, though the control system on that is far from ideal.

In the case of JRPGs, I think that Lufia II is pretty good. While not story-centric like more modern offerings, it has something that totally dunks on just about any other rival: Interesting dungeons. They are very much like 2D Zelda games, with a fair number of puzzles that require the correct application of tools and mind to resolve.

If you have any liking for RTS, then my opinion is that Total Annihilation is a perfectly playable old title. There is also a free remake out there, that probably adds a lot of 'modern-day' quality-of-life features.

I would argue that that game is more of a puzzle/RPG hybrid rather than a pure RPG simply because of the number of puzzles in dungeons and the presence of mechanics that solely deal with puzzle solving (like a special class of items that you equip via wheel and use outside of combat (the only one with non-puzzle uses is the one that stuns enemies) and a spell whose sole function is to reset the puzzle in the current dungeon room you're in).

Also, I don't think it's ideal for acquiring a taste for older games, as it has some more modern features, like IP attacks and a decent (by JRPG standards) interface. If you want to get used to older games, I would suggest playing games from well before then.

(Also, from a combat perspective, and ignoring that optinonal Ancient Cave minigame (which borrows elements from roguelikes), the game is too easy.)

Ultimate Doom.

Then if you want challenge, Plutonia (part of Final Doom).

If you're going to try Doom, be sure to use GZDoom source port. That way you get modern UI/controls.

JRPG-wise - can't really think of anything on the PC. I'm not much of a console gamer, but as already recommended, Lufia 2 is pretty easy to get into. Also Final Fantasy 4 and 6, and Chrono Trigger shouldn't pose any problems.

Try Diablo - the game that started a whole subgenre. Not sure how easy or hard it is to get to run with modern setups though. Last I tried it was on Windows XP, and it didn't like it if you had more than 1 monitor.

I would recommend the graphic adventures of Lucasarts. Many of their games in GOG are only sold in their remastered versions, but there are some in their moriginal format.

Another vote for Doom. Most of the puzzles on any of the maps is just finding a switch or finding a key. Missions are short and to the point, kill all demons. If you need a boost in graphics, there's a few free engines on the internet that you can use with the original files (Doomsday Engine, zDoom, etc.). To this day I will still load it up occasionally and play my way through.

Quest for Glory is a pretty good RPG. It's primarily a point and click game, but the storyline is pretty good, and you can import your character into the sequels so you retain your skills and items. Since it's the same character in each game, references are made throughout the series of your prior encounters/events.

If you want taste of old classic rpg then Baldurs Gate is the choice Fallout 1 and 2 are good too. As for old shooters Doom and Wolfenstein 3D + Spear of Destiny would be great. For a racing game Carmagedon series is great. For platformers you can play Jazz the Jackrabbit 1 or 2. Thief series is awesome for old stealth games.

And completely raped graphics..

For people who want to experience the game more or less as it was, but with mouse look, I'd recommend crispy doom first, then perhaps prboom+. But chocolate doom is surprisingly playable.

If you haven't done so already, you should definitely play Trails in the Sky, then Trails in the Sky SC, then Trails in the Sky the 3rd. The first two are great, the 3rd is good. They absolutely own 99% of more modern/mainstream RPGs to a ridiculous extent. They are also from the same developer who made Xanadu Next.

I also recommend all of their other stuff, such as the old Ys games. It's very hard to go wrong with any of their games.

I remember a game called retro city rampage. If you get into it you can see many things from other things like there is Batman in the game but named something else Joker is Jester. But many people don't like it. It is made in modern age but its like old games.I enjoyed but didn't finish it.
Pst it becomes real hard on some missions.

The graphics are as "raped" as you want them to be. GZ Doom doesn't force high end filters, texture packs or 3D Models on you. They're only there as options.