Traditional publishing formats like newspapers and magazines offer good examples of how to apply a visual hierarchy to fonts. They combine fonts in way that visually separates different textual elements like headlines, sub-headlines, body copy, and captions. Qualities such as size, boldness (also known as weight), and spacing (including leading, the space between lines, and kerning, the space between letters) all contribute to how the eye should navigate the page and what text should attract attention first.
When combining fonts, you do want contrast, but you don’t want conflict. Just because fonts are different doesn’t mean they will automatically work well together. Generally speaking, typefaces that share a couple qualities — maybe they have similar proportions, or the lowercase letters have the same height (known as x-height) are more likely to look harmonious together, even if the overall appearance differs.
Using typefaces from the same family is always a safe bet; after all, they were created to work together. Look for families that come with a range of options (different weights, styles, cases) to ensure that you have enough variation for your purposes.
When pairing fonts that come from the same family, you have to plan carefully to create contrast, varying things like font size, weight (such as light, regular, and bold), and case (upper, lower, small caps).
Choosing fonts that are too similar (i.e., don’t have enough contrast) becomes problematic. You’ll have trouble establishing a hierarchy, because the fonts aren’t visually distinguishable from each other. And any differences that are discernible may look more like a mistake than a purposeful choice.