Brawlhalla, and its free

There are so many things to suggest but first I leave this here so you can check which games your GPU can handle:
https://www.systemrequirementslab.com/cyri/

Edit: One time install will be enough.

i advise you to use game debate website to check compatibility to ensure which games you can run on your current hardware. It's very helpful!

Undertale is great, as is Defender's Quest

But rather than us listing individual games, look for games that don't specify a graphics card requirement, or specify that they'll work on Intel Integrated graphics (which is equivalent to your GPU).

I'd highly recommend checking out some older titles.

As far as I'm aware, you can run Fallout: New Vegas on it, which is a total gem of a game. Obviously, older Fallout games are also doable. Check out Oblivion, Morrowind. If you're willing to go even further back, check out the original Deus Ex, which is awesome.

If you're not into RPGs, then perhaps you want a more chill game, in which case go for The Sims 2. That game's one of the only ones that has made me look at the window and say "Oh damn, the sun's up".

Basically, odds are you can run anything that came out 2005-2006 and before with any later games needing you to check.

Witcher 3
Actually, you can also try previous parts of The Witcher.

Here's 10 games I could quite happily keep playing forever, none of which are very demanding nor expensive:
FTL
Heat Signature
Prison Architect
Civilization V
Starbound
Stardew Valley
Stellaris
Streets of Rogue
Terraria
Titan Quest

Try to get an RX 590 if you are in one of the regions where it is essentially the same in price as the 580. If the difference is over 7-8%, then forget I said anything.

Heartbound, Return of the Obra Dinn, Papers Please, Forager, Hollow Knight, Naruto´s figthing games, Overlord, The Witcher 1 and 2, Shantae games, Subnautica, Rain World, Ori and the Blind Forest, Life is Strange, Dead Cells, Watch_Dogs, etc... As you can see there´s a lot of games out there.

Suggestions for New to PC Gaming... Hmmm... let's see...

1. Start bitching about Epic Games Store
2. Ask when the next Steam sale is and then say, "My wallet is ready."
3. Register on a dozen different gaming forums and post there all night and day instead of gaming.
4. Spend a bunch of money on hardware upgrades which you post about, and then complain that you're broke when you post invite-only giveaways to a train of $1 bundle games
   Hmmm... I know I'm forgetting something...

Oh, yeah!

5. Start complaining about the dumbing-down and consolization of PC gaming. Quickly follow up by moaning about microtransactions, pre-purchases, cosmetic DLCs, Denuvo, and remasters that should be free for owners of the original game.

I think that'll get you up to speed nicely.

Welcome!

First, please don't get an AMD card. Why would you want something that is objectively less efficient, creates more noise, emanates more heat and on top of all of that is more expensive (or, depending on region, less expensive but due to the aforementioned reasons not worth it)?

Second: There is a wondrous world of all kinds of games... To be honest, most PC exclusives would be ones that don't require a crazy good PC.

What genres do you like?

I can suggest Rimworld, for example.

Here are some of my favorite PC games that should be able to run (I'm currently using a potato computer also)

Dragon Age Origins
Stardew Valley
Papers Please
Portal 1 + 2
Oneshot
Left 4 Dead 2
Borderlands 1 + 2 (best with a friend)
Saints Row 2 + 3
Lisa
Rakuen
The Banner Saga Trilogy
Oxenfree
Battle Chef Brigade
Cook, Serve, Delicious
The Cat Lady
Rogue Legacy
Pony Island
Wuppo
Stanley Parable / the Beginners Guide

Other's I haven't played but heard they are great:
Starbound
Celeste
Darkest Dungeon
Spelunky
Hyper Light Drifter
West of Loathing

Crusader Kings II

The only game you'll ever need.

I recommend this post, lots of great recommendations there:

https://www.steamgifts.com/discussion/TpRDr/modern-games-that-run-on-a-potato-machine-small-gib-added-level-1-basic-sg-ended

I have adored Civilization 3 and Railroad Tycoon 2 for years (over 1 decade), and neither demands tons of resources.
Mount & Blade Warband is also quite good,
Medieval Total War Gold
Turmoil.
Ticket to Ride
Crusader Kings II is good.

You can't go wrong with classic FPS games. Doom, Quake, Duke Nukem 3D, Heretic, Hexen, Shogo. I'll even throw in Eradicator, which deserves a little more attention than it gets.

FTL
Into the Breach
LYNE
One Way Heroics
Paint it Back
Shovel Knight
Spelunky
Warframe

I play on a mac which isn't the best gaming machine haha. I can't play some of the new big AAA titles that often seem to value graphics above gameplay anyway, but I can play most older games and many recent indie titles.

I've been playing without issues

Hollow Knight
Yooka Laylee
Dust An Elysian Tail
Torchlight
Stellaris
Civilisation IV (V and VI work fine as well)
Cat Quest
Bastion
Life is Strange
Talos Principle
Oceanhorn

That's just a few. I have 100s of games that run fine on my machine. :)

If you want to check out games I would recommend going to this site: https://www.systemrequirementslab.com/cyri
Type a game in and click Can I run it, the site will then first download a application it uses to get your computers specs, after that you can search any game the site has in its database and see if your setup can run the game :) nice way to see if you should or shouldn't buy a game based solely on if your PC can run it or not.

Bindings of Isaac games