When I started touring I had a 10-speed Raleigh, the cheapest rack I could find at a department store, and homemade rear panniers. I suspended my sleeping bag between the drops on my handlebars with nylon string. It worked fine.

You said you were going somewhere near Big Basin. Henry Cowell? I camped there once when Big Basin was full, but I've been to Big Basin many times; it's one of my favorite parks. There are some nice, long rides on dirt roads, and some excellent singletrack. It also tends to rain and be cold there when the surrounding area escapes the precipitation. Be prepared for wet, cold weather. What that person said about putting everything in trash bags is probably good advice.

Have a great time!