For a better recommendation some more info would be good, how much are you willing to spend? You also need to find out what's in the pc as that is important when upgrading only certain components. The PSU can only support a certain amount of power demand for example, if you download a program called Speccy, it will tell you what is in your pc. I can vouch for the fact that it is a safe program as I use it myself. Once you have that post the specs here and we can give you some more in depth recommendstions, but for now I'll give you a general idea.
For video editing a powerful processor and ram is key, especially for the high end stuff so I would recommend an i7 processor and at least 16gb of ram if you are willing to spend that much.
For gaming all you would need is to upgrade the graphics card, especially if you buy the processor and ram I have mentioned. I have the nvidia gtx 1060 and can recommend it as a good bang for your buck card which will run all current games on very high settings. Though if you're going full performance and cost then why not go for a 1080.
Like I said that may depend on the current set up which might limit your options, post your specs and I'll do my best to give some specific recommendations :)