Keep in mind, this is a matter of preference, and the answers here are going to give you a look at the choices and the member's view on the positive/negative for each one.
My opinion is to put 20% down (to avoid PMI) if the bank will lend you the full 80%. Then, buy the house, move in, and furnish it. Keep track of your spending for 2 years minimum. It's the anti-budget. Not a list of constraints you have for each category of spending, but a rear-view mirror of what you spend. This will help tell you if, in the new house, you are still saving well beyond that 401(k) and other retirement accounts, or dipping into that large reserve.
At that point, start to think about where kids fit into your plans. People in million dollar homes tend to have child care that's 3-5x the cost the middle class has. (Disclosure - 10 years ago, our's cost $30K/year).
Today, your rate will be about 4%, and federal marginal tax rate of 25%+, meaning a real cost of 3%. Just under the long term inflation rate, 3.2% over the last 100 years. I am 53, and for my childhood right through college, the daily passbook rate was 5%. Long term government debt is also at a record low level. This is the chart for 30 year bonds.
I'd also suggest you get an understanding of the long term stock market return. Long term, 10%, but with periods as long as 10 years where the return can be negative.
Once you are at that point, 2-3 years in the house, you can look at the pile of cash, and have 3 choices.
- Choose to pay the mortgage down. This would pull the payoff date to less than 10 years out, as the payment was based on such a high loan. This, in effect, is getting a 4% return on the money, and if that mortgage was bothering you, really takes it to less than half, and much sooner to zero.
- Take advantage of the rate rise. Not a prediction, but at some point, rates will bounce back. Putting into treasuries or CDs at a rate higher than the 4% you borrowed at would be great.
- Invest it over time, and get comfortable with the market's volatility. 10%/yr CAGR long term is less attractive to many people than a fixed 4%, guaranteed. This is the fundamental choice you have. Not a recommendation, but an example, DVY, the top Dow Dividend stock ETF, yields 3.28% at this moment. After 15% dividend tax rate, 2.79%. In effect, you are able to invest this money, and for a net cost of .21% get the gains (or loss?) of this ETF over the next decades. In the killer decade of 2000-2009, this 'bad idea' would have cost you 3% (total) of the amount invested. And since then, the market has come back so high, the dividends alone provide a very positive cash flow.
We are in interesting times right now. For much of my life I'd have said the potential positive return wasn't worth the risk, but then the mortgage rate was well above 6-7%. Very different today.