Depending if you're interested in learning more about real estate, I would use that $160k to invest in a multi-family property or 5+ unit commercial property which unlocks commercial loans and either cost in property management or do it yourself. That way, your mortgage is getting paid down by renters, you're hopefully cash flowing well which is building more wealth, and the property should appreciate over time.
If you're not interested in doing it all yourself, you could partner with another investor who's great at finding deals and/or managing the property and you can provide the financial equity. You obviously split the profit in a partnership, but it could be much more passive if you have less time or interest.
As for how much to put down, it depends on how much tolerance you have for loans. But financially, it typically works best if you use as much debt as possible as it adds more momentum to your investment and allows a higher rate of growth.
Sharon Lechter said recently that if you put $10k down on a $100k property and the bank loans you the rest, you still own the depreciation, the appreciation, and the tax benefits of a $100k property.