I am trying to make a map of administrative units in a state. I have a list of ~10 million addresses with a variable indicating which unit they fall into. My plan is to geocode the addresses using an Amazon EC2 instance or similar geocoding solution, map the points and then draw polygons around the sets of points.
Given my relative inexperience with GIS, I am wondering if there is a more sensible way to approach this problem. The addresses are quite clean, with zip codes attached (sometimes zip+4), and 99% or more of the addresses should be clustered together correctly in a single contiguous polygon. But I anticipate that after geocoding some addresses will fall outside the logical bounds of the polygon and need to be corrected post hoc. Each unit will have ~1200 addresses geocoded on average, with significant variance. My address list represents approximately 40% of all addresses within the units, so the points I will have to work with are quite dense.
Is this the only way to approach the problem? Note I am a grad student, so any solution needs to be cheap or free (my budget is under $300).
Edited to add: All addresses are in a single US state. I am working in ArcMap 10.4 and even figuring out how to use an API has been tough. My addresses are just in a .csv file and I eventually want a .shp file. I am a statistician, not a GIS professional, unfortunately.