Your PC that you found in the trash has better specs than the first one I installed Linux on a few months ago as a newbie: 770, maybe an i5.

Pop OS was super user friendly for a new user and handled drivers and everything really well for me. I've only played some less intense games from my steam library, but I'm not noticing any severe lag. I bet it could handle retro gaming/emulation easily.

That hardware isn't even bad, was top tier at the time and still will play any DirectX 9/10/11 game you throw at it at 1080p.

Linux runs great on my i5 4690k and GTX 750 Ti, so you're all good with 4790 and GTX 970.

EDIT: with 16GB RAM you're golden, happy gaming

It doesn't really matter unless you install a distro that's not using Plasma or Gnome. Just pick one of the popular distros, and you're good to go. CachyOS, EndeavourOS, Bazzite, Garuda, you name it.

I have a laptop with almost those exact specs. I maxed out the RAM (just because I'm a memory goblin), and I'm currently running Bazzite, Nvidia version. Runs everything great!

Feel free to DM if you have questions.

ETA: I opted for the KDE version, since it has better multitouch support than Gnome.

If your confidence level is decent (you said elsewhere you're new to Linux), I'd suggest EndeavourOS. Nearly all the benefits of Arch without most of the hassle. It's great for gaming and great as just a daily OS (whereas Bazzite seems very focused on gaming).

If your plan is emulation, Bazzite makes setting up either EmuDeck or RetroDeck very simple.

Just make sure to grab the Nvidia driver variant.

You can pick from KDE or Gnome, Bazzite does both.

A whole main, original thrust of Bazzite was to make it much more simple to set up emulation on a SteamDeck, uses a 'everything is flatpaks' approach by default, to keep things simple.

I run Bazzite on my Deck, works great for emulating older games, running modern games, I even set up a debian environment inside it via DistroShelf to do more complex dev type stuff.

With those specs, you should be able to run HL2 or a PS2 emulator just fine, I'd think, just keep the resolution at 1080p... maybe somethings you could take up to 2K, still be at or over 60fps, basically for games released prior to ~2006/7/8?

@korendian i7 4790 here with an Nvidia GTX 1060. Bazzite Nvidia booting to the normal Plasma desktop performs fantastically! You don't say if it's SSD vs HDD, but if it's the latter, put in an SSD and it'll be great!

Depending on how open you are to be tinkering with the system I would suggest Arch since it can be very lightweight as a base and then use reteroarch for the emulation (but I'm not sure about the wii emulation...)

Install Lubuntu. A lightweight Ubuntu derivative.