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How much would you expect to pay for a new or used 2jz alternator for a 1993 supra, and how much would you expect to pay for a alternator rebuild?

my car is currently at an AA repairer who does auto electrics, just hoping the cost doesn't sting me too much

The repairer is best placed to provide you with pricing and options. I wouldn't know what you'd need to pay for a brand new alternator for a vehicle of this age, but my thinking is that is would probably be very expensive.
I'd say your best option would be to have the auto-electrician provide you with an estimate to repair your own alternator.