Your problem seems pretty straightforward. Grab files from ftp or network drive, unzip and import them into your geodatabase. I would likely wrap the steps in a batch file, where I would run the move and unzip through command line and then call the python script to work the GIS magic.
Stack Overflow - Moving file locations through command line
Stack Overflow - Unzipping files through command line
You'll want to use the arcpy.FeatureClassToGeodatabase_conversion method to convert the shapefile (see Feature to Geodatabase - ArcGIS help page):
# Name: FeatureClassToGeodatabase_Example2.py
# Description: Use FeatureClassToGeodatabase to copy feature classes
# to geodatabase format
# Author: ESRI
# Import system modules
from arcpy import env
# Set environment settings
env.workspace = "C:/data"
# Set local variables
inFeatures = ["climate.shp", "majorrds.shp"]
outLocation = "C:/output/output.gdb"
# Execute TableToGeodatabase
In addition, you'll probably want to make sure that you are running some form of scan or virus protection on anything coming from outside sources.