This work generalizes the Age-of-Information (AoI) minimization problem of {\em update-through-queue} systems such that in addition to deciding the {\em waiting time}, the sender also chooses over which ``channel’’ each update packet will be served. Different channels have different costs, delays, and quality characteristics that reflect the scheduler’s selections of routing, communications, and update modes. Instead of considering only two channels with restricted parameters as in the existing works, this work studies the general $K$-channel problem with arbitrary parameters. The results show that {\em both the optimal waiting time and the optimal channel-selection policies admit an elegant water-filling structure}, and can be efficiently computed by the proposed low-complexity fixed-point-based numerical method.