What board to use to send a text message via an arduino board
The GSM Shield will suit your needs. This is a shield, meaning that is a board that will go on top of another Arduino board (e.g UNO, Leonardo, ..., choose whatever you'll need).

This is what it will look like:



To send SMS you'll also need a working SIM card and the GSM library to program the shield. On the previously linked page there are some tutorials to follow in order to check the basic functioning of the setup.