RetroGaming

Looks like a couple people mentioned this, but you will likely want/need to mod whatever system you get. I have a modded NES and Atari 7800, so I can comment on those.

There used to be a NES mod that fixed the pin connector issue, called "Blinking Light Win" https://www.arcadeworks.net/products/blw?variant=36483581116569. They've been sold out for at least a couple years (I've sporadically checked out of curiosity since I bought mine). But if you can get your hands on one I strongly recommend it. It has made my NES incredibly reliable and it's very easy to install. No soldering, just open the console, remove the 72 pin connector, and pop in the BLW. Done.

For the Atari 7800, there's a composite video/s-video board mod you can pick up. I'm forgetting what the name of it is, and I don't have the manual handy at the moment, but I will try to update later with the name and link. Anyway, this one is more involved and requires some soldering. It's not too difficult, just requires some patience, and it's very worth it. Composite audio is a separate solution, but doesn't require extra hardware, just a little more soldering.

I hope that helps! Feel free to reach out about these mods and I can explain further.