Fonts are the most important visual tool in design. They are the perfect shoes for the outfit. Use the wrong shoes and you kill the look. Although there are thousands of fonts and we could talk about them until the end of time, we are keeping it simple by separating them into four main categories: Serif, Sans Serif, Script and Display.
Serif: These fonts have "feet". They are considered more serious or traditional. Traditionally, these fonts were preferred for reading because the serifs made it easier to navigate visually helping your eyes along the lines of text. However, this is not true of the digital pixel world, where sans serif fonts are easier to read.
Sans Serif: Sans Serif literally means without serifs. These fonts don't have feet. The extra little lines on the end points of the letters. They are considered more modern and cleaner.
Script: These are the fonts that we think of as cursive or handwriting.
Decorative/Display: These fonts are just that: decorative, novelty, display... meant to get your attention. They are to be used with discretion and sparingly to bring attention to a word or a tag line only.
Typography (the use of fonts) provides the first impression to the public that you are trying to convey your message to. Fonts can convey a feeling or an attitude. You might be trying to convey fun and games and yet your project yells boring and secure. Fonts were designed for specific purposes and in specific design periods. These design periods defined a feeling or a political movement. If they were meant for the Russian revolution, you might not want to use them for a baby shower invitation. A script, can't be used as a book, website content, or magazine text.
Decorative or Display fonts are never good for reading long lines of text. These fonts demand our attention. They are the equivalent of all caps in a text. They can be fun and can have many uses. But used incorrectly, they can kill your design.
Think about the message you want to convey. Who you are conveying it to. What do you want people to feel when they see your project?
Then we can go into legibility, color, size, etc. But, that is another matter. For now, think about your font and you will have a better end project.