This guide misses a few things: after removing the old display, you will need to remove the silver backing/shield, the home button and the camera (be very careful when pulling the copper tape from the silver panel so not to tear it.) You will then need to place these in the new display. This is another 9? screws or so. I think the iPhone 5 page has this guide (it's pretty much the same thing.)
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I always order the cheapest displays from Amazon (about $30 right now with free shipping for Prime members.) They always work just fine for me -- none of these parts is "officially from Apple" (they're all Chinese knockoffs.)
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On a further note, be VERY careful when plugging the new screen to the mainboard - the FPC connector pins can BEND and BREAK if you force the connector. Broken pins require very careful hot air/reflow soldering of the mainboard and a new FPC connector: not recommended for novices!