We are Sydney based and have done a round trip cruise from Sydney through the closer Pacific Islands of Melanesia to French Polynesia and back to Sydney.
Getting through Customs is not a major delay UNLESS you decide to ignore the warnings about not bringing in any food or plant products - including those lovely apples you may be given on board the plane. The sniffer beagles will suss you out, you will be pulled up and may be fined. Taxis are readily available at a rank that is usually managed by a supervisor. About $50 - $60 AUD for a taxi to the CBD. There are shuttles - easy to find - the signage in the airport is quite good even for the jetlagged. Hard to advise on a hotel without knowing your price preference and whether you are prepared to pay for location. I would go for the Holiday Inn in the Rocks area for mid range, the Rocks Youth Hostel for cheap and really good - twin rooms with all facilities not all dorms - and my favourite the Park Hyatt if you are really splurging or have the right credit points. There are lots more - but for location aim for the Rocks or CBD area.