I've not tried this yet, but I would be curious to know if you could just use the CHIP ENABLE pin on the ESP8266 instead of the GND pin. That would allow you to use a cheap 2N7000 to control the pin.
I guess I need to determine what chip enable does for you... power-wise. (maybe not so much)
I'm going to avoid engineering speak as much as I can.
Don't forget that MOSFETS are transistors... they just have a slightly different behavior.
People like MOSFETS because they are generally better at voltage switching as "ON-OFF" devices due to really low "ON" resistance and that they will not require a base(gate) resistor (which only costs pennies... but still seems to annoy people that it's needed with BJT).
I personally have no bias against BJT as a switching device but what I commented on in the earlier post above is a valid use for an N channel MOSFET that is rated for "logic-level" use.
Note: BJT Transistors only need a small current at the base and only a sip of voltage (for a kludge value... think anything above 1V is enough to make it work). MOSFETs on the other hand require gate "Voltage" above a certain threshold before they will "switch" fully on. That's why you need one that is rated to "switch on" at logic levels such as 5V.
Many commonly available MOSFETS, like the Radio Shack variety IRF510 require at least 10V at the gate to work right, making them impractical to be driven by a pin. So make sure the parts you buy are logic level if you want to drive them with an Arduino pin.
However you switch your IC you must first ensure that you aren't trying to drive any
signals to it at the wrong voltage, or you will get large protection-diode currents flowing
as the devices self-powers through the signal pins.
Normally you would high-side switch as this doesn't disrupt your groundplane on a PCB.
You then have to ensure all signals to the IC are either LOW or high-impedance before
powering the IC down.
With a low-side switch like you propose you'd need to ensure all signals are either HIGH
(3.3V) or high-impedance before powering it down).
Using a logic-level p-channel MOSFET or PNP transistor is more normal due to the
common ground-plane in typical circuits.