It depends on the type of sound that you are looking for when you are strumming....
For a smooth sound, I absolutely agree with the above posts.....also consider using a nylon pick....they are a little softer.
For a more percussive attack, I use a heavier pick...usually something like a Dunlop .88 to a 1.25....but be aware that using a 1.25 can be hell on your strings if you play hard. It can also slow you down a little until you get used to it. But choke up on the pick, only allowing the very end to protrude.  You can also vary this to adjust the sound, a tight grip on the pick will allow you to tighten up your sound.
Also, if playing on an acoustic, like the other guys have mentioned before...the placement of the pick over the hole is also important. Near the hole is going to give you the most often desired sound...closer to the neck will help soften the tone. A neat thing I like to do is to play near the bridge....it produces a lot more of a "harp" like tone....try dragging the pick backwards over the strings near the bridge on your favorite chords. It's cool!
Ultimately try all of these techniques and then you will naturally gravitate towards the styles that work for you.
Good luck learning!!!