I would argue that you have to make a decision like this in the context of your overall investment/cash flow strategy. If you have yet to come up with a financial plan, that's where you need to start.
Putting down more money can make sense in many situations, such as not liking to be in debt. Or living in a state that protects one's home against creditors/lawsuits but doesn't protect other investments like bank accounts and taxable accounts. Or being a person whose road to hell is paved with good intentions to save but who won't actually save much money unless forced to.
As for the supposed tax break, well, paying zero interest handily beats getting a 33% deduction on whatever interest you pay. So I wouldn't make the decision to take on a mortgage for the purpose of getting a tax deduction for it. Though of course if you're going to take the loan anyway, you should certainly take advantage of the deduction.
As for number of years, again, opinions differ. Some people argue for extending such relatively cheap loans for as long as possible. Others argue with taking the shortest loan so that you pay less interest (including, typically, getting a lower interest rate). Again, you need to think about this in light of your larger financial picture. For example, if you want to be able to retire in 10 years, a 30 year mortgage is probably not the best move.