Look, the simple answer is that there is no single best peripheral: it all depends on preference. I am going to give you a list of things to consider when buying gaming peripherals, but I can't pick ones out for you.
However, saying that I can say that the best TYPE of gaming keyboards are mechanical. Very often, you will se mechanical gaming keyboards that light up a.k.a they are RGB. Don't waste your money on those, RGB does not add anything to the actual keyboard apart from lights.
There are many types of mechanical keyboard switches: Cherry MX and own brand switches. Razer for example uses its own switches. Cherry MX come in different colours, and the different colours signify different specifications of the switches. For example, Corsair use Cherry MX Red, which means that the keys don't make a sound when you hit them. Research the kind of switch you want before investing in a new keyboard.
Good brands for keyboards: Corsair, Razer, Steelseries, Logitech (speaking from personal experience).
Gaming mice are much more personal preference than gaming keyboards. Certain mice are designed with different grips for different people. Certain mice are designed for different games. DPI is also a factor when buying a mouse. Once again, do more research to make sure you know what mouse you want to buy.
Good brands for mice - Logitech and Roccat (speaking from personal experience, I have used both the Roccat Kova and the Logitech G502 and find the logitech to be better value)
Gaming headsets have less variation, although still have some. Speakers in headsets vary, and you can get Stereo, real 5.1, real 7.1 and synthesised 5.1 and 7.1. Some games however do not let you use 7.1, CS:GO is an example of that. Do more research on the type of speaker you want.
Good brands for headsets - Razer, Logitech, Kingston. I think the HyperX Cloud II from Kingston is the best value for money however (speaking from personal experience).