P mosfet or N mosfet
First design criterion here is VGS, which is the voltage on the transistor's gate with reference to the transistor's source.


For a P-MOSFET  VGS needs to be lower than 0V to make the transistor conduct current;
For an N-MOSFET  VGS needs to be higher than 0V to make the transistor conduct current.


Second design criterion is that you want the internal diode reverse biased:


For a P-MOSFET VDS must be lower than 0V;
For an N-MOSFET VDS must be higher than 0V.


Notice that VDS = -VSD.

Depending on the architecture of your inverter you want the Source of the transistors 


at the power rail, either VCC or GND, (most likely for an inverter) or 
on the output rail (most likely for an analog amplifier stage).


So you:


connect a P-MOSFET with its Source to VCC and you pull the Gate voltage to GND and it starts to conduct. Connect the Gate to VCC and it stops conducting
connect a N-MOSFET with its Source to GND and you pull the Gate voltage to VCC and it starts to conduct. Connect the Gate to GND and it stops conducting.








simulate this circuit &ndash; Schematic created using CircuitLab

Also notice that a MOSFET need a threshold voltage VGS,TH on its gate to slightly start conducting, which is usually in the order of several volts. So the higher or lower from the first paragraph is not entirely accurate, but it works getting the picture. The actual voltage to get the MOSFET in saturation is much higher, in practice you want to pull it as high as possible.

There are quite a few gotcha's with MOSFETs, the most important being:


Its gate capacitance that will slow down the rate of change of the gate that you try to pull up and down;
Maximum current as written in the datasheet is only under theoretical optimum conditions: http://www.mcmanis.com/chuck/robotics/projects/esc2/FET-power.html
Check the datasheet if the internal diode is rated for the current in your application, otherwise use an external diode.
Beware of ringing as a result of the gate capacity and the connecting wires (however short they are). You proabably want to use a small series resistor to dampen the ringing.
Keep controller to gate and controller to drain connections as short as possible. These are the major factors in speed of switching.
Use a controller that supports dead time. This means that during switch over both transistors are momentarily cut off, before the other one is driven into saturation.


Check the datasheet of your MOSFET for details.