My first thought is that a house is not an investment. It is a means of providing shelter, which is a necessity. Yes, house prices may fall, but so what? That only matters when you decide to sell, and prices will almost certainly rise back at some point (or you'll just have to absorb the loss).
Yes, prices might fall, but they might continue to rise as well.
So what you should be comparing is the cost of buying and maintaining a house versus the cost of renting. If the interest spent on a mortgage is significantly less than the rent, and you plan to stay in that area for many years, then it is in your best interest (financially) to buy a house. If not (because interest rates are high or house prices are high, or both), then yes continue to rent for a while until prices go down or you can afford a larger down payment.
As for what to invest the cash in, there are plenty of questions here that can help with that, but if you intend for the cash to be safe for a down payment on a house, then make sure that you're investing in things where you can absorb a drop.