The best APCs in League of Legends that can work in the bot lane, are the ones that have the sustained damage like Cass or Corki!
The battlemage class of champions in LoL is hard to master and the best ones have a lot of magical DPS, from a short range, such as Ryze and Cassiopeia.
Mages such as Syndra, Vex and Zoe, are the best burst mages in LoL, as they easily delete an enemy in one skill rotation, with their high single-target burst!
Damage over time, or DoT, is dealt by only 7 items in LoL, with options for a pure tank like Sunfire Aegis, to pure mages, such as Liandry's Anguish.