First, I would sit down and crunch the numbers on what my tax liability on that $300k would be after the all the other income I'd already earned and was projected to earn for the tax year, and set that amount aside . It would really suck to go out and spend all of the $300k, only to find out later that the IRS demanding their share of it. If anyone can figure out how to get blood from a turnip, it's the IRS. I don't want to be that turnip.
Next, I'd pay off my remaining credit cards and student loans. Such things are drags on my monthly cash flow that I've lived with for far too damned long, dampening my ability to accumulate short, medium and long-term savings.
Then, I'd take a hard look at my level of emergency savings. Do I have enough to survive a short to medium term interruption of cashflow from my usual sources (job, etc)?If not, I'd fill them up until I could. If yes, I'd skip to the next step.
If I held a mortgage on my primary residence at this point, I'd consider paying it off entirely, or a large chunk of the principal so as to significantly shorten the reamaining time until the loan was paid off. This I'd have to consider carefully. House mortgage loan interest is tax deductable, and there's some good arguments that one can get better returns on investment by not paying off one's house. I'd have to do some soul searching to determine if such potential gains were worth having the debt hang over my head, or if the reduced stress of owning where I lived free and clear was preferable.
After that, I'd max out my tax-advantaged reitirement accounts for the year, be they 401(k)s, IRAs or HSAs.
Once that was done, I'd stuff the remainder into my taxable investment account.
A final small sliver would maybe go towards a nice steak dinner with a tasty bottle of wine or a good beer.
Then I'd probably keep living my life as though nothing ever had happened, continuing to earn as much as I can and save as much as I can, until my goal of Fuck You Money was achieved.
But that is what I would do. What might work best for you may differ.