Just bought a new 50s road worn Strat. The bridge is flush to the body. Is this correct or should the back end of the bridge be raised off the body surface?

They were designed to float about 2mm from the body, although some people deck them.
Loosen the spring claw screws to correct this, should you so wish.

Thanks! The claw screws- are these the two long screws under the back cover?
And nothing needs to be adjusted on the top side of the bridge?

That's them.
You may have the adjust the bridge saddle heights to give the required strings heights.

Read this:

http://www.fender.com/support/articles/ ... etup-guide

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Bill