One would usually use "fast" to describe an activity that takes place over an extended period of time, such as running or driving; "quick" to describe a single activity, such as a hand gesture. These are not absolute rules. As I wrote, they overlap.
However, to say more, we'd need to know more about the context in which you plan to use one or the other. Please tell us.
In general and outside of idioms, they are not far off interchangeable but, to me, 'Fast' implies overall speed of motion, 'quick' implies a [sudden] shorter movement and also often indicates a short time.
"It was a very quick interview." = Only few questions were asked, it lasted only a short time.
"It was a very fast interview." = The questions came quickly, one after another.
"It was a very fast car." = it had a high top speed.
"It was a very quick car." = it can accelerate very well.