This number uniquely identifies you to the government. However, they will probably give you a toll-free phone number to obtain your SSN over the phone in a few days. The initial period may seem to be rather expensive to you especially if you come from a country with a currency not as high as the dollar. Bring enough money to last you a month and some initial expenses. International checks will take forever to come through.
Most bank drafts are convenient too, but all in all travelers checks are a better bet.
It covers most aspects of your health care except for dental and eye care, and pre-existing conditions. It would definitely be cheaper to get a complete dental and eye checkup in your home country before you come here. Also, in case you use corrective eyeglasses or lenses, it may be a good idea to get a spare set. Even if you did not earn US-source income you will usually have to file an Income Tax Return. These workshops are highly recommended, as the U.S. and California Tax Returns can be quite difficult to understand.