The best way depends on what your goals and time scale are.
Stocks are generally riskier, but potentially more profitable than bonds, and a simple savings acount has virtually no risk but low profit. Within the categories, there are riskier and less-risky choices.
As you draw closer to needing the money, (e.g. retirement or college), you should shift more and more of it into more stable forms so that you don't lose it to a sudden shift in the markets just before you need it. Long-term, however, the riskier investments are more likely to give you the most reward.
All of my investments are in stocks (mutual funds, specifically, which tend to be less risky but vary depending on the particular fund), but that is because I have around 40 years to retirement, and won't have any college expenses for at least 2 decades since I don't have any children yet. Your situation sounds like one that requires a bit more of a safety net.
This article has some details, but there are others our there, many of which can be found by typing something like
investment risk stocks bonds into a search engine.
From what I understand (although, not being in the market for a house, I'm not well-informed on the subject), you're unlikely to find a better time to purchase a house than now, as far as the larger economic picture is concerned. That, of course, needs to be balanced with your own economic situation.
Two last things:
You didn't mention any credit card debt, but since so many Americans carry one its worth mentioning that putting money toward paying off a credit card debt now will usually leave you with more money than investing now and paying it off later.
I think the economy in general will improve, but interest rates will certainly rise (and have already begun to) so the effect on your personal economy may not be positive.