The cerebral cortex is a complex and highly organized laminar structure, containing different types of neuronal cells. The spontaneous activity patterns exhibited by the cortex depend on the intrinsic dynamic characteristics of its neurons and is affected by mechanisms of synaptic plasticity. This work presents a downscaled version of the Potjans-Diesmann cortical microcircuit model composed of up to three different types of neurons connected by synapses that obey different spike-timing-dependent plasticity rules. The model is studied under different combinations of neurons and plasticity rules. The results show that the type of inhibitory neuron has a strong impact on network firing rate and synchrony, and this impact is enhanced by synaptic plasticity. However, a heterogeneous composition of inhibitory neurons has a controlling effect on rate and synchrony.