Baten, my S just finished his first year at Stanford and we are from the midwest. H, S and I flew to SFO for move-in day, and my H and I used one suitcase for the 2 of us, and the other 5 bags were for S's stuff, one of which was a printer. We wished we had waited to get the printer in Palo Alto. He used 2 rolling duffel bags, which fit easily under his bed in the dorm. The other bags were canvas that just fold down and fit into the duffels. There was a pretty big closet that he shared with his roommate, plus 3 dresser drawers for his own use. My S had space left over for storage. You can get anything you need in stores near Stanford that would be difficult to pack - printer, fan, etc. I'd recommend bringing your sheets/towels so that you can wash them ahead of time. If you'd like to buy them when you get there, that's ok too. You can easily rent or buy a fridge, microwave after you get there and discuss it with your roommate.
I'd recommend trying to get there as early as you can on move-in day, since there are so many people ready to help you on that day - from carrying bags up to your room, getting your computer set-up to Stanford's wireless network, picking up your bike and so on. There are special sessions for parents on different subjects, and a convocation welcoming freshmen and transfers. It is a wonderful day.
Check the
Campus Bike Shop site for info about renting or buying a bike. My S bought a bike from them and it has worked out well. You can store your bike for the summer with them, too.
Shipping stuff can be as expensive as checking bags on a flight. I'm not sure where you would have it shipped, but someone at Stanford can tell you. You can get your ticket whenever you want, as long as you know what day you'll be arriving.
My S has a Mac, as do the majority of students. But plenty of them have PCs. You can go either way. His laptop did everything that he needed a computer to do.
Think real hard about taking books. My S took the maximum # of hours and didn't have much extra time to read for pleasure. On the odd occasion that he did, he went to one of the many libraries and read books and magazines there.
I'm sure your move will all work out fine. Stanford gives lots of guidance about what to bring and how to get what you need. Good luck!