It's easy to get confused when you change dozens of fonts. To understand typography / pairing / hierarchy first of all choose 2-3 fonts (depends on your design / concept) and pretend you don't have any other fonts available.Try to make that fonts looks nice accordingly to the hierarchy rules and your concept.
Here some easy to pair fonts combinations:
- Oswald + Ubuntu
- Steelfish _ Source Sans Pro
- Ubuntu Titling + Open Sans
- Abraham Lincoln + Oswald
- Blanch + Intro Free font + Oswald
- Code + Myriad Pro
- BP Diet + Oswald
- Muncie + Steelfish
- Trajan Pro + Oswald
As you see I like Oswald allot :).
Of course you can use many other fonts but it's a helpful exercise working with just few fonts. This exercise force you to concentrate on hierarchy and composition.
From my experience I can tell you, any font can be pair any font in the right context.