Graduate Teaching Assistants (GTAs) often receive little training in pedagogy before leading undergraduate courses and labs at large, research-focused universities. Though most universities offer some teaching-related professional development to GTAs, opportunities vary in quality and accessibility. The caliber of instruction provided to undergraduate students can influence those students' persistence in a chosen major and retention in the college or university. This study characterizes the teaching-related concerns of a large cohort of novice GTAs from STEM and non-STEM graduate programs over the course of their first semester as a GTA. New GTAs completed qualitative and quantitative surveys during their first semester at a large, research-focused university to elucidate their changing teaching-related concerns. A subset of these novice GTAs participated in focus group interviews to generate a rich data set regarding their apprehensions related to teaching. Previous teaching experience at the K12 or college level was correlated with greater confidence in ability to perform teaching-related tasks, while post-graduation plans that do not include teaching were correlated with lower confidence in GTA ability. International students tended to be less confident in their ability to locate resources to support their roles as GTAs, and the confidence gap between these GTAs and peers increased over the course of an intensive two-day TA Orientation. New TAs' greatest teaching-related concerns include maintaining high energy levels in the classroom and balancing teaching-related responsibilities with other professional and personal roles. Areas of least concern included being close in age to undergraduates, handling communications from undergraduates' parents and communicating in English. The conclusions of this study will be used to critically evaluate the professional development opportunities currently offered to GTAs and build new, relevant teaching-related trainings when necessary to meet the diverse needs of GTAs identified in this study.