I would run the ground wire and not depend on conduit. If you are going underground, you want to use the gray PVC anyway.
May I suggest a ground rod at the garage? Nothing wrong with driving an 8' rod into the ground and connecting your box ground to it as well as the ground from the house.
You know that transformer out on the telephone pole that provides your power? Well, that neutral wire is not grounded out there. They ground it at your house. That way you are assured of good neutral to ground in your house....that is also why they want your ground to include your plumbing.
As for the box in the garage, what you put there will depend on what you pull from the house. If you have a 220Vac panel then I would run 220 to the garage, say 40 amps? At the house, you will have one double circuit breaker...it looks just like two circuit breakers tied together. In reality, they are 2 110Vac breakers giving you 2 110Vac lines. Connect between one of those lines and common and you have 110v....connect across both 110 lines and you have 220Vac.
In the garage you want another box with 2 or more breakers in it. If you are going to run anthing 220, then you want a 220 breaker (double) for that circuit and everything else single breakers. I prefer to have seperate circuits for lights and outlets. I like to be able to kill the power to the outlets so I don't have to worry about little ones turning on the table saw when I'm not around....but then again, I know my oldest will never do that again.