I took the Guild workshop at slate run and white oak was selected as the wood. The instructors chose it for rot resistance as the structure is open on two sides among other things. Depending on you needs that may be very important or less so.

The wood was all VERY green and easier to cut than I expected. It was VERY heavy too.

White oak does have a high shinkage, if the building is unheated this will lessen the "violence" of it's movement. For whatever reason Burr Oak is excluded from the strength tables for generic red/white oak.

Eric