When I've put out games in the past, there have usually been two goals in font selection:
- Fonts that are easy to read at the angle the player will be looking from.
- Fonts that evoke the setting of the game.
For example, The Golden Wilderness is set in colonial California, so a typeface that was widely used in the 1700s helps evoke the setting. There's basically nothing you need to read during the game that isn't upright and in your hand (and that you have plenty of time to read), so readability isn't the issue.
Leaving Earth, on the other hand, has many cards sitting all around the table that need to be understood by the players. Readability helps the game play more smoothly, so a clean font that's easy to read from multiple angles is needed.
Which particular fonts meet these criteria for your game all depends on the specifics.
Acquiring those fonts is another matter. There are plenty of free fonts out there, but don't be afraid to spend a little money on a good, professional font. The best professional fonts are designed with an eye for many tiny details (like kerning and ligatures) that you (assuming you're not a typographer) shouldn't have to worry about.
If you're just using a font for a bit of flavor, things like kerning might not matter too much (though it pains a typography enthusiast like me to say it). If you're using a font for your main title/logo, or for extended blocks of reading material, those small details matter much more.