Credit scores are based a lot on your available credit and your demonstrated ability to repay debts. Available credit is typically how much unused credit is available on your credit cards.
Advice: PAY AS MUCH AS YOU CAN - AS EARLY AS YOU CAN
In my eyes, Student Loans are evil. Life has a way of happening, and next thing you know, you'll be 30, or 40, and still paying off your Student Loan. Student Loan default rates have never been higher - and you don't want to fall into that category - that will surely affect your credit in a bad way.
Lastly, think of it this way - say your loan is for $5,000. Yes, the wonderful government is paying the interest now, but 6 months (or whatever the end of your grace period is) you will be charged interest on that $5,000. If you pay $100 a month now, then at the end of that same 6 month period you will only be charged interest on $4,400. ($5,000 - 6 mo * $100).
One more thing - check your credit for free here: https://www.annualcreditreport.com/cra/index
I suggest checking it 3 times a year using a different credit reporting agency each time. Checking your credit regularly (and generally browsing of the sites) will teach you what affects your credit and what doesn't.