Integrated photonic spectrographs offer an avenue to extreme miniaturization of astronomical instruments, which would greatly benefit extremely large telescopes and future space missions. These devices first require optimization for astronomical applications, which includes design, fabrication and field-testing. Given the high costs of photonic fabrication, Multi-Project Wafer (MPW) SiN offerings, where a user purchases a portion of a wafer, provide a convenient and affordable avenue to develop this technology. In this work we study the potential of two commonly used SiN waveguide geometries by MPW foundries, i.e. square and rectangular profiles to determine how they affect the performance of mid-high resolution arrayed waveguide grating spectrometers around 1.5 $\mu$m. Specifically, we present results from detailed simulations on the mode sizes, shapes, and polarization properties, and on the impact of phase errors on the throughput and cross talk as well as some laboratory results of coupling and propagation losses. From the MPW-run tolerances and our phase-error study, we estimate that an AWG with R $\sim$ 10,000 can be developed with the MPW runs and even greater resolving power is achievable with more reliable, dedicated fabrication runs. Depending on the fabrication and design optimizations, it is possible to achieve throughputs $\sim 60\%$ using the SiN platform. Thus, we show that SiN MPW offerings are highly promising and will play a key role in integrated photonic spectrograph developments for astronomy., Comment: Accepted at Applied Optics, Special Issue on Astrophotonics (24 pages, 13 figures, 3 tables)