Well when first starting yes some pain is normal, but continuing pain may not be normal, if you are really really just beginning then do 15-30 mins a day or if you're as pain tolerant as I was, till you couldn't feel em anymore lol (trust me don't do this).
C chord is always going to be a hard chord, especially when just starting, remember your fingers have never really been in that position before, using muscles and such you've never used before.
A couple of threads are good for the chord thing:
One is by Kirk on the begineers lessons, watch the little videos when he's playing you will see the proper position.
True beginner? Here's a lesson for you!
And I would also like to direct you to a thread where I discussed some of the proper forms when first starting that way you lessen injuries and are able to continue to play and have fun with it, instead of wincing in pain.
Ahhhh my fingers are screaming at me
There are some general tips in this thread.