We consider the joint optimization of sensor placement and transmission structure for data gathering, where a given number of nodes need to be placed in a field such that the sensed data can be reconstructed at a sink within specified distortion bounds while minimizing the energy consumed for communication. We assume that the nodes use either joint entropy coding based on explicit communication between sensor nodes, where coding is done when side information is available, or Slepian-Wolf coding where nodes have knowledge of network correlation statistics. We consider both maximum and average distortion bounds. We prove that this optimization is NP-complete since it involves an interplay between the spaces of possible transmission structures given radio reachability limitations, and feasible placements satisfying distortion bounds.We address this problem by first looking at the simplified problem of optimal placement in the one-dimensional case. An analytical solution is derived for the case when there is a simple aggregation scheme, and numerical results are provided for the cases when joint entropy encoding is used. We use the insight from our 1-D analysis to extend our results to the 2-D case and compare it to typical uniform random placement and shortest-path tree. Our algorithm for two-dimensional placement and transmission structure provides two to three fold reduction in total power consumption and between one to two orders of magnitude reduction in bottleneck power consumption. We perform an exhaustive performance analysis of our scheme under varying correlation models and model parameters and demonstrate that the performance improvement is typical over a range of data correlation models and parameters. We also study the impact of performing computationally-efficient data conditioning over a local scope rather than the entire network. Finally, we extend our explicit placement results to a randomized placement scheme and show that such a scheme can be effective when deployment does not permit exact node placement.