Good question. I'm a novice landlord, and I'm interested in what other people recommend as best practices.
I agree with the poster above that the #1 thing is to keep a separate account for your rental.
I would strongly recommend that you not put that check in a personal checking or savings account. As your rental business gets more complicated (deposits, repairs, depreciation, taxes, insurance, additional rentals) you will want to be very clear about what money belongs to the rental account and what money belongs to you.
I live in Washington State as well, so I get to keep any earned interest or appreciation. I put the rental deposit and last month of rent into a separate taxable investment account and buy VTI. I am not worried about liquidity for that account. Should the tenant leave early I can cover the deposit and last month. Should the tenant not leave early I will get replacement deposit and last month from the next tenant. I want the rental property to make money through (possible) appreciation, cash flow and investment of cash. In my HCOL city the deposit & last month is ~$7,000. That is more than I want to leave in an unproductive account.
My goal is to use the property and cash to make more money, then I'll buy another rental property.
I'm interested in feedback as well.