Once I start working full time we would pay as much as we could afford each month on the mortgage in order to pay it off as quickly as possible.
If this is just a starter home, you will most likely get more for your money if you invest it instead of paying down the mortgage because you will only be in the house a few years.
For example. Paying an extra $500/month on a mortgage for 4 years will cost you $24,000 but may only save you $1200 in interest, especially with rates so "low". But if you take that money and put it into a VERY "safe" account that only returns 3% per year, you're looking at closer to $1500.
But this obviously just an example. Your own situation may be different, but I suggest you look into how best to use your money.