System default is the GPU default used by all applications, Power Saving is for a lower-power GPU (usually an integrated video such as Intel graphics), High Performance is for a higher-power GPU (usually a discrete graphics card from somebody such as AMD or NVIDIA). If your system only has one GPU, then you will see the same GPU name in both Power Saving GPU and High Performance GPU options.
GPU power is generally reflected in the price, so it is not necessarily worth buying a gaming-specific graphics card unless you are interested in running games on their highest settings, and want the best possible performance per dollar. If you are going to be playing games such as The Witcher 3, you are going to want to make sure that you are getting a top-of-the-line video card. If you are building a Gaming Computer to be able to play games on 4K Monitors, you will want to make sure that you get a higher-end graphics card.
If you are going to be playing games with a laptop, you will also need one that has a discrete GPU. If you are going to perform any kind of professional tasks on your laptop, like editing videos or doing graphic designs, you will want to get a laptop that has a discrete GPU. When considering discrete GPUs, then, you will want to look at both the amount of memory the graphics card has as well as the amount of throughput it provides.
Most graphics cards will include the recommended power size (in Watts), and you will also need to take into account how much power is being drawn from the other components of your PC. Note that when designing your PC or choosing to upgrade a graphics card, you will also want to look into how warm any given graphics card runs when running at its highest power. If you are looking to build a high-end PC for competitive gaming, and need a monitor with high refresh rates in order to get the edge over the competition, then you will probably want to go with a high-end graphics card that can handle high refresh rates.
Just like your monitors resolution, your GPUs maximum refresh rate will significantly impact GPU performance. If your monitor has a triple-digit refresh rate, you are going to want a powerful card and CPU to fully realize it. This means you could have the most powerful GPU on the planet, but if your monitor is only 1080P, then you are never going to use all of your graphics cards capabilities.
If you are not interested in playing high-end PC games with your GPU, then you can save yourself quite a bit of money by opting for a cheap, entry-level graphics card instead. The model of GPU usually dictates what RAM is installed on a graphics card, so once again, when you pick the GPU that is best for your needs, you will be getting the correct RAM to go along with it. If you are using a desktop PC, the GPU will be enclosed within the graphics card you connect to your PC; if it is a laptop, the GPU will be embedded directly on your laptops motherboard.