the min. The safe thing to do is to keep that extra cash for a rainy day. As you get bonuses and raises then you can pay down the principal of the loan if you want.
But again, the responsible thing to do is to keep as much cash as you can on the sideline and buy the house with the minimum downpayment.
Also I'll add that very few people stay in their first home for 30 years or more. You really should consider getting a 5 or 7 yr mortgage.