Very simple, very straight forward, but potentially expensive:
(1) Do not entrust your car to someone who does not know there way around a 350Z.
(2) Find a specialist to provide you with an informed diagnoses and an estimate.
(3) If the estimate is for an engine rebuild, then weigh up the cost of this against a known low mileage pre owned engine.
(4) Remember that an estimate is exactly that, the specialist will only provide a written quotation once the engine is removed and stripped.
(5) Very rarely will you get away with just piston rings, so build into the estimate the price of 6 new pistons.
(6) For guidance, depending on the diagnoses, the worst case scenario will be 2k - 3k
(7) If service history is unknown, be prepared for extras ie: clutch and fly, valve guides, chains, tensioners, oil pump etc.
Preowned engines are in stock at the minute, and all engine rebuild parts are also in stock.
Just drop me a PM once you have your diagnoses/estimate if I can help further.
Alex.