To turn things on/off over the internet I use one of these $100 boards.
**broken link removed**
There are several similar boards for sale.
The output is 0/5 volts that need a transistor and relay to drive your motor.
You will need to learn a little about the internet and TCPIP. The board comes with software that works and will do what you want. I modified that software to get a home control system working. (I don't know much about HTML programming) See my system at
gradllc.com/internet.HTM
(This is a copy of my system not the real thing! I don't want you turning lights on in my house)