Switching off / power saving

Hi,
I am building a device, which checks sms messages every few hours and has to run for a month or so on a 4Ah LiPo battery.
Now an Atmel328p in sleep mode controls the phone bit fine, however the phone (Adafruit Fona) is drawing 25mA when just connected and switched off.

So I thought I use a 'digital switch' to switch off the power for the phone when in sleep mode.

What would I use for this? MOSFET? logic level gate MOSFET? Transistor? Relais? bearing in mind that the phone can draw up to 2A for a short time.

And what are the advantages / disadvantages of each?

Thanks for any advice

Logic level p-channel MOSFET as a high-side switch - find one with 0.05 ohms or
less on resistance and it'll be quite capable of 2A indefinitely. You can use a fairly
large gate resistor like 10k to slow down switching and reduce high current pulses
due to the Fona board decoupling capacitors charging up (you want to prevent
crow-barring the supply).