I am fairly new to arduino boards and I was wondering which board to use. I was looking into the edison board because it has built in wifi and bluetooth.
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.
Another option is the Spark Core or Photon. It's not an Arduino but it's very close. I have Arduino sketches that I have ported right over with no modification.
The Spark boards are internet-connected and you can send text messages or emails using IFTTT. It's also going to be a lot more cost effective than an Arduino plus wifi shield, particularly if you can wait until June for the $19 Photon to ship.
You could also use a Raspberry Pi connected to the internet to just do the email part but that's a little more trouble than it's worth.
Actually, you should use a Raspberyy Pi if your project involves complex processing in it.
But if the project is very simple, just use one of those Spark Core or Photon.
Using an Arduino and a Sheild to do it is certainly not a good idea, as the Pi is much faster in processing and costs about the same.