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We present studies for optimizing the next generation of ground-based imaging atmospheric Cherenkov telescopes (IACTs). Results focus on mid-sized telescopes (MSTs) for CTA, detecting very high energy gamma rays in the energy range from a few hundred GeV to a few tens of TeV. We describe a novel, flexible detector Monte Carlo package, FAST (FAst Simulation for imaging air cherenkov Telescopes), that we use to simulate different array and telescope designs. The simulation is somewhat simplified to allow for efficient exploration over a large telescope design parameter space. We investigate a wide range of telescope performance parameters including optical resolution, camera pixel size, and light collection area. In order to ensure a comparison of the arrays at their maximum sensitivity, we analyze the simulations with the most sensitive techniques used in the field, such as maximum likelihood template reconstruction and boosted decision trees for background rejection. Choosing telescope design parameters representative of the proposed Davies-Cotton (DC) and Schwarzchild-Couder (SC) MST designs, we compare the performance of the arrays by examining the gamma-ray angular resolution and differential point-source sensitivity. We further investigate the array performance under a wide range of conditions, determining the impact of the number of telescopes, telescope separation, night sky background, and geomagnetic field. We find a 30-40% improvement in the gamma-ray angular resolution at all energies when comparing arrays with an equal number of SC and DC telescopes, significantly enhancing point-source sensitivity in the MST energy range. We attribute the increase in point-source sensitivity to the improved optical point-spread function and smaller pixel size of the SC telescope design.