We have just put in an offer for our first home. If accepted, we are planning to put in atleast 20% downpayment (800K sales price and 160K downpayment) and take a loan out for the rest.

Last year 2013, we got hit by the AMT. We will likely get hit by AMT this year as well and the next and so on

Our question is this - We are trying to figure out how much downpayment to put in (20% or 25% or 30%)?
Putting more downpayment will as a consequence reduce our monthly payment and interest over the years.

Will that make us pay much more in AMT over the years? Because we have less mortgage interest to deduct?

On the investment front, given that interest rates are at low levels (4.15-4.35%), isn't it better to just put 20% downpayment (just to avoid PMI) and invest the remainder (10%) in stocks/mutual funds?

Any first order thoughts on the above?