I think you have 2 scenarios:
Inflation: your best hedge is the 30 years fix loan to buy the house, house prices will increase with the inflation and you debt will be eroded.
Deflation: Here the problem is that you end with an asset that will lose value over time and you have payments to make with money that is more valuable everyday. I believe this is the zombie apocalypses scenario. I think you should try to use a FHA loan, really low down payment and keep all the cash possible in hand to use it in case of emergency. I think deflation will be a brief period, with a 30 year mortgage you will not have a problem as long as you keep making your payments so keeping cash in hand is your hedge. I think it will be a brief period because the government will try anything to avoid deflation, you may end with a free house....
In both cases as long as you can make the mostly payments comfortably, you should use the lowest down payment possible, think on a typical 25% down payment, if you believe inflation is more likely, take a FHA loan 5% down and use the rest of the money to buy something that will appreciate with the inflation (PM, Bitcoin?, rental property). Otherwise, take the same FHA loan and keep the additional 20% in cash (or cash equivalents).
Just my 2 cents.