That link will have all the information you need to plan your trip. We went outside of permit season (meaning we didn't have to make a reservation, still had to get a permit) and that worked well for us. I spent around $500 total: ferries to/from Washington, gas from Oregon to Washington, hotel in Port Renfrew one night, permits, meals off trail, meals on trail, trail bus, etc.
I want to go again...it's amazing.
“Twenty years from now you will be more disappointed by the things you didn’t do than by the ones you did do. So throw off the bowlines, sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.” – Mark Twain