Hi, I'm a newbie here and will be installing my first wood floor. I'm using solid 3/4" x 3 1/4" White Oak and will be putting it down to a 1/2" plywood floor. Boards will run perpendicular to the joists. It's a second floor. From my research it sounds like 16g cleats are preferred over staples so thats what I plan on using. I'd like to know what the recommended length of the cleats should be? My local supplier has 1 3/4 " long as smallest.

1/2" Plywood subfloor seems a bit thin. What's the support structure under it?

2x12's - 16" centers

Your fine. 3/4 is recommended but 1/2 in good enough. If you have enough height to add another layer of 1/4 or 3/8 you can.