Assuming that you realy know how to finger pick , this (alternate picking) is similar to the succesive p,i picking (using alternate index and middle finger picking)..
for arpeggios , you may need to use similar picking (down strokes or up strokes) for succesive strings , this is similar to something called 'sweep picking' which is a very hard to learn technique , used to shred on arpeggios...
Never think of this sweep picking now, and focus on alternate picking... when you feel alright with the pick , you can go on to higher steps..
the most important thing that determines your picking direction (up or down), is to use the least amount of movement to save your energy for higher speed, so give your mind some job ...
also, there are 3 ways of moving your pick:
1 - moving your whole arm, this only helps for chord strumming
2 - moving your hand . to change from one string to another, & chord strumming
3 - moving your fingers that hold pick. for more than 1 note on a single string. (this one is the hardest, a lot of people tend to move their hand even for a single string picking.. it's o.k. but always remember that the less movement saves more energy)
Finally, the most fundamental rule of learning music, always begin at a slow tempo, rising your level gradualy, and never move to higher level unless you are completely comfortable with your level.
