There are two obvious choices to enclose the joists & add soffits. (approx 350 sqft soffit area)
First is simple white planking running perpendicular to the house. Lots of material options but probably something similar in width to the 6″ decking – 1x6s or even 1×6 from exterior ply with small v notch. White keeps it bright.
Second is wood-stained planking similar in shade to the decking. Again, many wood spices to choose from but none are inexpensive.
Any thoughts, additional ideas, etc?