The minimum wire size allowable would be 10 gauge. For a 75 foot run however, the voltage drop would be 5.31 volts. This exceeds the NEC recommendation of no more than 3% (3.6v) so while it is not legally required, for best efficiency, you should run 8 gauge.
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A #8 copper or #6 aluminium conductor will limit the voltage drop to 3% or less when supplying 30 amps for 75 feet on a 120 volt system.
At the service entrance you will need AWG 1/0 gauge.
Depends on the size of the service. 100 amp service will require 3 gauge, 150 amp service will require 1/0 gauge, and 200 amp service will require 3/0 gauge.
As a service entrance wire you need AWG # 3/0 gauge copper.
3/0 gauge
I would recommend you use 1/0 gauge