Screws or nails for securing 2" lumber to overhead joists as fireblocking?
2X12 is great, 3/4" plywood would be easier to handle and to drill through when you need to. Chalk your plate line where the wall will go on the room side, rip your plywood to go to the basement wall and 1/4" shy of the chalk line. That way when you set your upper plate you can still see the line to accurately set your wall.
To answer your question, using nails will work, it is only fireblocking, you only really need enough to keep it up, since it is not structural, but do it anyway. Screws would work better, especially if it needs to be adjusted after it is up in place, and you see it needs to move a bit, it does happen. Shear or expansion should not be a concern. material usually shrinks once installed.