Either build works.
Universal knowledge: Poppy's abilities are all magic damage. Regardless of what you build you NEED spell pen if you want Q to really hurt.
AD: AD boosts your Q's damage the most because its just 1:1 where as AP scaling is lower. Trin force + Hextec gunblade are very popular for AD poppy players then building the rest tanky with one spell pen item.
AP: Boosts your Q slightly lower than pure AD but you generally get more AP than you can get AD so it evens out in a long game. The key difference being that you have deathfire's + a REALLY strong E. This turns poppy into an assassin.
Personally preference for me is AD. Trin force really bumps up your Q damage. Its nice to use Ult in a defensive method too instead of charging in murder one person then die.