Cortical neurons are versatile and efficient coding units that develop strong preferences for specific stimulus characteristics. The sharpness of tuning and coding efficiency is hypothesized to be controlled by delicately balanced excitation and inhibition. These observations suggest a need for detailed co-tuning of excitatory and inhibitory populations. Theoretical studies have demonstrated that a combination of plasticity rules can lead to the emergence of excitation/inhibition (E/I) co-tuning in neurons driven by independent, low-noise signals. However, cortical signals are typically noisy and originate from highly recurrent networks, generating correlations in the inputs. This raises questions about the ability of plasticity mechanisms to self-organize co-tuned connectivity in neurons receiving noisy, correlated inputs. Here, we study the emergence of input selectivity and weight co-tuning in a neuron receiving input from a recurrent network via plastic feedforward connections. We demonstrate that while strong noise levels destroy the emergence of co-tuning in the readout neuron, introducing specific structures in the non-plastic pre-synaptic connectivity can re-establish it by generating a favourable correlation structure in the population activity. We further show that structured recurrent connectivity can impact the statistics in fully plastic recurrent networks, driving the formation of co-tuning in neurons that do not receive direct input from other areas. Our findings indicate that the network dynamics created by simple, biologically plausible structural connectivity patterns can enhance the ability of synaptic plasticity to learn input-output relationships in higher brain areas.