Self-hosting is always nice because you can remove the reliance on an external asset, so one less network request to make. You can download and host Google Fonts yourself, and the built-in Discourse font options are also sourced from Google and don’t rely on their servers.
As mentioned, having the fonts served from your site directly is better for performance (though fonts are usually small so it’s not a major concern). Try to not include more variants and styles than you need, usually two different fonts with normal and bold weights is plenty.
Mostly watch out for fonts that are really light in appearance, and if your site has a dark mode double check that for readability too… sometimes the color scheme can make a big difference. Try zooming in/out in your browser and changing the font size in your user preferences to make sure nothing unexpected happens.