I would use the same airfoil at root and tip and with washout at the tip, because it is a simple, safe and proven thing to do.

If you use a symmetrical airfoil at the tip without washout that might not come out as it should, the NACA 0016 have poorer stall capacity than the 2415 so you should actually end up with more washout to prevent tip stall at takeoff and landing than with just 2415.

If you want to benefit from the use of different airfoils at the tip and root the characteristics of the tip airfoil should be the same or better stall capacity and at the same time produce less lift than the root, that is a quite complex thing to achieve and you will likely still end up with at least some washout at the tip if you want it all to be "correct".

Tryggve