I'll just contribute a bit here on the buses to get things moving. Yes, buy the 7 day (or whatever) tickets. I think, if I remember right, that an adult ticket entitles a child to travel free.. so particularly good value. My daughter uses them when she comes across, even if she brings the car, as the kids find it part of the fun of the holiday, and she doesn't have to drive.
Don't forget we also have steam trains, electric railway and horse trams. You can get all the way up the Mountain on a Victorian train... an experience not to be missed.
All the info on public transport is available in the Sea Terminal, where the boat drops you.
Welcome to TTwebsite, and look forward to seeing you while you are across.