5v would be my choice.
If you're using dimensional lumber from lumber yard, I'd go with 2x6 for a 12’ span. If using ruff cut, you might get away with 2x4. If it sags, you'll have to add a center beam with supports.
If you're using dimensional lumber from lumber yard, I'd go with 2x6 for a 12’ span. If using ruff cut, you might get away with 2x4. If it sags, you'll have to add a center beam with supports.