It’s an awful time to buy a house. The market has NOT bottomed out yet. Give it a couple of years.
In the short term, I’d recommend one of the following to park your money. These aren’t meant to earn much money; their mostly just a very safe place to store money (safer than a bank since you’re over FDIC limits) until you figure out what to do.
http://www.treasurydirect.gov
https://personal.vanguard.com/us/funds/snapshot?FundId=0050&FundIntExt=INT
The second one I believe invests 100% in treasuries and is more liquid than purchasing treasuries outright.
Long term it’s up to you, but I’d point out that right now is a lousy time to invest if you are not extremely knowledgeable. Volatile bear markets are difficult to play in.
Finally, keep in mind that $500k is not a lot of money. You are not RICH, you just have a comfortable nest egg. It’s very tempting to start spending as if you are rich, and that money will disappear faster than you think.