Suppose an ice hockey puck strikes a hockey stick that lies flat on the ice and is free to move in any direction. which
quantities are likely to be conserved: angular momentum, linear momentum, or kinetic energy (assuming the puck and stick are
very resilient)?

Linear momentum

Explanation:

The most likely conservation candidate is the linear momentum. The law of momentum conservation states that the sum of momenta before and after an (elastic or inelastic) collision will remain constant.

The kinetic energy is another possible, but less likely suspect. It is conserved in elastic collisions (i.e., those with no kinetic energy loss), but we are not told this collision is assumed elastic. In fact the real setup would be nowhere close to an elastic collision, as the stick lies on ice, which hasn't be zambonied for an entire period of rough skating, there's rough surface and the stick's shaft is also slightly stuck to the surface through frost. So when the puck hits the stick, a portion of its kinetic energy is spent to unstick the stick and get it moving. And so, kinetic energy is not conserved.

Angular momentum is not applicable with the puck-stick scenario.  

not too sure thinking all accelerations are pointed down