For the mosfet i would use a mosfet driver ,doesnt matter really if you choose microchip or the IR21xx series.
With just 5 volt you get a mosfet open but its heels over the canal open with the resistor pushing the source up with rising current i prefer a gatedriver and put 12 to 18 volt on the gate this way your always guaranteed of a fully opened mosfet .
Choice of mosfet doesnt matter much with low currents like this ,although i must confess i never use logic level fets .
With automotive fets as cheap as they are ,i think why bother 4.7 mOhm sounds good 300 Ampere max. cant hurt
(i do like that you have the mosfet on the positive side ,i use to do that myself for more accurate measuring)
About the opamp you can do with a standard non inverting amplifier since your measuring is referenced to ground there's no need to do difficult .
(if its usefull to you electronics workbench has a opamp wizard then you can generate the amplification and schema needed)