More than 20% down payment for income property?

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I am not looking to flip or do anything short term.

I want to buy a rental property for between 400k-2 mil, and I want it to produce positive cash flow and be extremely low risk.

I am in Southern California, and would *probably* like to buy here, but I am willing to explore other areas.

I am not ready to do this now, but am looking at the 6mo-2yr time frame.

I am thinking of putting a large amt of cash down (over 20%) and trying to maximize my cash flow while minimizing my risk.

Has anyone tried this strat? What are the details I should look out for? What is a better strategy for low risk vs a better strategy for high return? Pay 100% of 400k? Pay 20% of 2 mil? Something in the middle?