And then the mortgage. That would be my sequence. Paying off all debt doesn't have to include the mortgage, but I would advise that it include the mortgage. There is something so incredibly freeing about being debt-free. Start educating yourself about investments.
People can learn about investments through courses, books or Web sites.
Read books by Suze Orman. She says you have to respect money, respect what it can and cannot do for you. If you respect it, then you will treat it much more kindly and not with such abandon. In the time between receiving the windfall and reinvesting, keep the money in money-market or mutual funds. Appreciate good fortune.