Also, with a MOSFET, no current limiting resistor need be applied at the base because no current flows, correct? So the output from the 595 can be connected directly to the gate of the MOSFET, right?
In a word, no.Firstly the IRF9520 is not a logic level device - it needs a 10V or more gate drive so some interfacing between the shift reg and MOSFET would be needed, but more fundamentally its no good for 10A. It might take 1.5A before overheating and perhaps 6A with a big heatsink, but 10A would have it dissipate 60W!
You don't say what voltage you want the MOSFET to control nor why you need a P-channel one.
QuoteAlso, with a MOSFET, no current limiting resistor need be applied at the base because no current flows, correct? So the output from the 595 can be connected directly to the gate of the MOSFET, right?Not really - the gate of a MOSFET is like a capacitor - a current flows until its charged up - power MOSFETs have capacitances around 1nF to 50nF or so. For high-frequency switching you typically put a few amps into the gate to make it switch fast enough. A current-limiting resistor is often used to prevent high-frequency oscillation. For low-speed switching this is less important - you can drive a logic-level FET direct from logic if you don't want high-speed switching and can cope with switching times of several us. A current-limiting resistor of 100 ohms or so will lessen the stress on the 595 output pin. Incidentally if the current through the source-drain circuit is fluctuating there will be current in and out of the gate since the gate-capacitance depends on the drain current. A lot of people don't realize this.
You seem to require a logic-level FET with a Ron of 0.05 ohms or better - its only the older MOSFET designs that have such high Rons, its not hard to find N-channel MOSFETs with Ron of 0.01 ohm and P-channel with 0.03 ohm.... Remember heat dissipated is I-squared-R. The current rating for a MOSFET is its least useful figure of merit since its always a power-dissipation limit with infinite heat-sink!