What is the best way to identify a notebook so that you can find the right documentation for the notebook on the manufacturers website?

model and serial number

Use the product number from your notebook sometimes found on the bottom on a white sticker (p/n) or by right clicking computer in the start menu and choosing properties.

Find your laptop's model number, it is usually on the bottom or sometimes behind the battery. Enter this on google or on your manufacturer's website. Sometimes forums dedicated to that manufacturer...

By the owner's name written inside the front cover.

The best notebook for you, depends on what you want to use it for. If you are a serious gamer then you will probably need to spend more money than if you just want it for surfing the net and chatting...