Airport Extreme 6th gen and my devices at home

Do I need to install something on my windows laptop in order to have a wireless connection with my airport extreme router?

Nothing else should be required for Windows 8.x computer to connect wirelessly to the AirPort Extreme. However, you may not be able to administer it as the most current version of the AirPort Utility for Windows only provides support up to Windows 7. Note: However, I am currently using it on my Win 8.1 computer to administer my 802.11ac AirPorts without any issues.

Apple also provides a return policy in case the new Extreme does not work out for you.

Simple wireless connection to the internet is occasionally problematic. It is often related to Intel wireless cards and poor drivers.. but you cannot predict the results.. ie test and see.

Apple routers do not support upnp and so somethings are issues..

Online gaming for example.

I have other devices at home such as the PS4

You will need to manually forward ports if you need to play games.. same on computers and wii.

Again you will not know exactly what you are getting into until you test it..

Apple do accept you have to open the box to test.. and will give you 14day return (double check in your country though).

The apple router might work better in combo with a more standard router.. but you haven't explained why you bought the AE over a more standard router so we cannot really comment on that.