I'm writing a medieval/fantasy story, and I wanted to know some facts about traveling on horseback and in carriages or carts. Generally speaking I want to know about the pros/cons of such travel.

Specifically:
-How far/fast/long can horses or carriages travel under normal circumstances versus what would be capable during emergency situations.
-Benefits of carriage travel, and the shortcomings. How much would carriage travel typically cost?
-Under what circumstances would it be suitable to just walk there?