Woodworker here. Framing lumber isn't dry and will move a lot while it goes from 19±% to 6 or 8%, in your house. If the annual rings are long gentle curves (looking at the end grain) the 2 x 12's will cup as they dry. Not good! Chose boards with the grain as near vertical to the faces as you can. They will stay flatter but will still shrink over their width. All wood will move until it reaches equilibrium with its environment. If the humidity in the room changes the wood will also. You can't stop it! Temperature has little effect other than affecting the absolute amount of water the air can hold. Framing lumber is usually "SPF" meaning it can be a mixture of spruce, pine & fir. If you are lucky you may find southern yellow pine, Strong heavy and hard especially after it fully dries. If there is a millwork shop near you they may carry it and will cut it to length for you. What they have will likely be random widths and be dried to 9-11%. Reasonably stable SYP. They will call it 8/4 or eight quarter (2" rough) Usually surfaced to 1 3/4" They can edge a piece for you also. I used to stock SYP so we could match the trim or flooring in old construction.
Whatever wood product you choose to use, treat both sides the same to prevent differential movement of the two faces and cupping. Saturating all surfaces especially the ends with a drying oil that you've mixed 1/3rd urethane oil based varnish in, gives a more durable finish than straight Danish oils like McFadden's or Watco. The finish will slow the exchange of moisture and reduce movement. Whatever finish you use it will become mared over time. Just part of its history.