Either is fine when you are just getting started. 

But it can help to consider your musical goals.  If you primarily want to play fingerstyle (fingerpicking, acoustic material, classical, etc.) then you should focus on using your fingers.  If you primarily want to play rock or blues styles (especially electric with riffs & lead lines) then you should focus on getting used to using a pick as soon as possible.

You can always start with one, then learn the other.

Hope that helps!