I would say you are missing a PC/mac. The PC/mac is needed to program your Arduino. 8) .....
....Och I missed you had not included your development environment on the drawing 8)
Also note that your modem must have a network cable plug. It is more likely you will have a router or switch to create a LAN which connects to the internet.
If you really mean to have a modem (so nothing else than your arduino connected to the internet), think about how you will be able to reboot the modem in case of failure.
Best regards
Jantje