I would definitely recommend keeping the down payment and closing costs in savings and not investing it anywhere. Like someone said, any place that'd give you short term returns is way too risky for you.
However you also mention that you are saving $40k for "emergency / home maintenance / furniture".
I'd separate emergency from the other two categories. What kind of emergencies are you expecting? Are you planning on waiving inspection contingencies that'd put you at risk of buying a house with major issues? Are properties in your areas typically old and thus more likely to have issues? How handy are you / capable you feel of dealing with some home maintenance on the cheap?
Depending on the answers to those and your overall risk tolerance (i.e. are you willing to delay buying furniture if liquidation is slow) I'd consider investing some of that $40k.