SSIS can also do this well along with SQL Agent to run the SSIS package. Either waiting for a file to appear in a folder or running at specified times is possible.

We deal with over 500 csv format files every day in both these ways.

I use a script task in SSIS to see if a file is arriving as some of ours are quite large and wait until it is fully available then for zip files,a For Each loop with an execute command task to unzip it into a folder with the 7zip tool before processing the csv files into the staging and then main reporting database and a File System task to move the processed files to an archive directory (script task if you want to create a dated one).

Package logging and error handling ensure you know when anything goes wrong.