Congratulations on buying your first home and for asking a great question. I can’t give you a blanket answer however. It will really come down to the rest of your financial situation. Your mortgage payment should be affordable, but not too comfortable. The first home is the one you should have to stretch a little to reach. Between your mortgage interest write off (which we hope is continued) and future raises, your payment will be more affordable over time.
If you are in other debt, car, credit cards, student loans, you may want to focus on paying them off first. The rates are generally higher and the value that those goods are on depreciates. If you don’t already have a safety net in the way of a savings account, I would go there next. Having several months of income in savings can help you keep your house if one of you loses a job or becomes ill and misses work for a while.
If you are otherwise debt free and have a great savings (emergency) account, then paying down your mortgage would be good. I think most people will find paying a little extra every month will have the greatest net affect. Every dollar over the minimum payment on a simple interest loan goes against the principle. As your principle decreases, the total interest you will be paying will decrease as well.
I hope this was helpful, congratulations again and best wishes for a great new year.