Whether you make it or buy it, your sink will not be big enough. From your sketch, it looks like you've budgeted about 7 ft. Go bigger. Plywood comes 8 ft. long. Use the whole sheet. Home Depot sells a polyurethane paint that works great. The instructions are long, but the product is fine, and when used along with silicone caulk, will make your sink absolutely waterproof without having to pay Marine Hardware prices.
I used a simple Home Depot cold water filters with both the hot and cold--call me a rebel! Check the filters regularly. You'll be amazed. I taught myself to sweat copper pipe, and the whole installation is compact and keeps chunks out of my wash water.