There a many different types or families of fonts. Script, sans serif, serif and decorative are just a few common ones. You can find a whole searchable listing of Google fonts and families here.
Fonts can serve many different purposed and convey different emotions. Be sure to think of the meaning when you are selecting a font.
Be sure to pick fonts that pair well together, either by being similar in nature or appropriately contrasting. The image at the rights shows several pairs that are either academic in nature or decorative. Make sure your fonts match your message and convey the desired tone or emotion. Fontpair.co for more examples of Google fonts that pair well together.