A number of battery-driven sensor nodes are deployed to operate a wireless sensor network, and many routing protocols have been proposed to reduce energy consumption for data communications in the networks. We have proposed a new routing policy which employs a nearest-neighbor forwarding based on hop progress. Our proposed routing method has a topology parameter named forwarding angle to determine which node to connect with as a next-hop, and is compared with other existing policies to clarify the best topology for energy efficiency. In this paper, we also formulate the energy budget for networks with the routing policy by means of stochastic-geometric analysis on hop-count distributions for random planar networks. The formulation enables us to tell how much energy is required for all nodes in the network to forward sensed data in a pre-deployment phase. Simulation results show that the optimal topology varies according to node density in the network. Direct communication to the sink is superior for a small-sized network, and the multihop routing is more effective as the network becomes sparser. Evaluation results also demonstrate that our energy formulation can well approximate the energy budget, especially for small networks with a small forwarding angle. Discussion on the error with a large forwarding angle is then made with a geographical metric. It is finally clarified that our analytical expressions can obtain the optimal forwarding angle which yields the best energy efficiency for the routing policy when the network is moderately dense.