This airport is the worst. It is a long drive to get there unless you live in east Mesa. It is very unorganized and checking in is usually a nightmare. We have flown out of this airport using Allegiant Air many times and we will not do it again.
The flights are cheap, but they nickel and dime you to death so by the time you pay for everything it's probably not much cheaper than using a real airline. Allegiant is even charging for carry on bags now.
Save yourself the huge headache and fly out of Sky Harbor.