Cheapest way to get motion sensor to send SMS or email
If your main constraint is how cheap something should be just use an old cellphone and connect it via serial port to a microcontroller (i.e. atmega).

If the microcontroller detects a motion via the motion sensor send some at commands via the serial port to send a sms.

Here is an example project http://www.8051projects.info/resources/sending-sms-through-nokia-3310-5110.47/

A secound solution which is a semi professional one with a little more costs, would be a raspberry pi with an umts stick (most of them can be used as gsm modem). You would than run a little python script which sends commands to the gsm modem. For this you could use gammu which also has a python bindings. http://wammu.eu/python-gammu/ 
But in this solution you have to connect a motion detector circuit to the Raspberry gpio.

Another but more expensive solution would be using a gsm board in addtion to a microcontroller circuit.. But these gsm boards are quite expensive.