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There is no such thing as a watt amp.
To determine wire size you need to know the current. Watts = Current x Voltage, so if you know the applied voltage to the load that consumes 300 watts you can get the answer. If we assume 120 volts as standard home voltage then current is 25 amps. If you had 240 volts it would be 12.5 amps.
In general 14 AWG is 15 Amps
12 AWG is 20 Amps
10 AWG is 30 Amps
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