A mix of tank and ap seems the best bet for Amumu, he is a very good tank, one of the best. His ult is incredible, he has a good stun, and he puts out wayyy too much aoe damage to be ignored in a teamfight. If you are up against a mostly physical team you can just stack sunfire capes and you are done. I find rushing a rod of ages is also pretty good for Amumu, it gives him his needed mana, more health, and ups the power of all his abilities.