For the trip from the airport to hotel, I'd advise you to take a taxi. It won't cost you more than $400 with the tunnel fees and the bridge toll. Don't worry about the luggage, the boot lid can be tied down.

Then your sight seeing would make a lot of sense if you each got an Octopus card for public transport. You can reload at stations, 7-11s, CIrcle Ks etc..