What you want to do is actually relatively simple. BUT there is one important limitation, so we'll deal with that first.
You can NOT expect the OS already installed on the WD 500 GB unit to work in your new system. Whenever an OS is installed on a hard drive, it is customized for the set of hardware (the computer) the HDD is installed in. The installation process does an inventory of all the devices in the computer (and there are usually 30 to 50, many of them components of the mobo itself) and ensures that all the drivers for them are installed as part of the OS. If you then attempt to install that HDD in a different machine and BOOT from it, there are two very similar problems: the new machine has devices for which the HDD does not have the correct drivers, and the HDD does have and load drivers for devices that are not present in the new machine. There is a process called "Repair Install" that can be run on the old drive when first installed in the new machine, but you need the OS Install disk for that OS version. It does not always work, but often does. If corrects all the driver mismatches and then the OS is re-customized to the new machine's hardware set. If you need to do it this way, look up "Repair Install" for Windows.
HOWEVER, the really simple way to move up to a new machine is to be sure that the new machine has its OWN NEW HDD, and you install a new OS on that. AFTER that is done and working you can shut down and install the HDD from the old machine into the new one and just have it used as a data storage device that you do NOT try to boot from. In this situation ALL of the contents of your old HDD is fully available to you. There is no need to Uninstall anything in Device Manager on the old machine.
You should be aware, however, that application software installed on the old HDD will NOT be considered installed on the new one. Installing an application involves making custom entries in the Registry of the machine. An application residing on the old HDD does NOT have any corresponding Registry entries in the new OS on the new machine's HDD. Your best route here is to re-install all your application software on the new machine on its C: drive, and then you can use all the data files and documents from the old HDD. To do this you may well need to check with the publishers of your app software to see how you can install it a second time on a new machine. No doubt they will need some assurance that it cannot continue to be used on the old machine at the same time.