Can you get a virus just for visiting a sketchy website?

Not with an uptodate browser. But there was malware in adverts on normal webpages. Even CIA recommends an adblocker.

Nowadays it is almost impossible to get a virus just from visiting websites. As for security recommendations I would recommend never running applications as roo that 100% don't need it, as for 3rd party repos I would always be a by mindful of the apps but generally there isn't too much of a risk, of getting a virus.

There have been cases of malware exploiting scripts and even images being displayed, whether directly hosted on the site or via compromised ads.

Highly unlikely. A site could try to exploit unpatched security holes in your browser, but if your browser is up to date, this is unlikely to succeed. Modern browsers are very complex and large so they have lots of weaknesses, but they also get fixed quickly, a lot of eyes are on their code and they utilize sandboxing techniques as well to isolate things from your system.
Still, it's a good idea to harden your browser further yourself, or run it in an additional sandbox.

Check Flatpaks as well.