First thing you'll want to do is select your CPU. This is very important, as the CPU, motherboard, and RAM must all be compatible or the computer will not work.
Once you picked your CPU, check its socket type and supported chipset and RAM DDR# & MHz. The socket type determines what boards the CPU will physically fit properly in, which will immediately narrow down the motherboard choices. The find a cooler that has mounting that fits the socket type.
Next, you'll look for a motherboard that has that socket type and chipset, and also supports the same RAM DDR# & MHz as the CPU. While a CPU can support one or two types of DDR, a motherboard will only fit one. The motherboard specs will also tell you how many GBs of RAM it supports as a max, though modern boards typically support 32, 64, or 128 GB, so that's not a concern if you're going with 16GB (which I'll add to the consensus of that being plenty for game + recording software). Also note the form factor (ATX, micro-ATX, Mini-ITX, etc.) as this will be important later.
For RAM, get the DDR# and MHz supported by chip and board, in whatever GB quantity you desire. Note: For best results with memory access efficiency, try to pair up DIMMs (the technical term for the sticks of RAM) that are the same speed and capacity, for dual or quad channel (which is basically your CPU looking at 2 or 4 sticks simultaneously for data). They don't have to all be the same model of DIMM, though doing so does throw all guesswork out the window. You also don't have to fill all the slots, either. Just 2 DIMMs for a dual channel board, the most common among 4-slot motherboards, is all you'll need to access the channel benefit. Just look at the motherboard's instructions when installing the matching set, put them in the Channel A slots, and you're good to go.
Graphics card... I'd agree with the above statements. With the 10xx series out, the 9XX Geforce GTX cards are coming down in price, so you can find a good bargain if you shop around, especially when they're on sale. 970, 980TI (the top of the line in 9XX series), or 1070 are solid options for price and power.
1 TB HDD is good for most gaming computers, but you're wanting to do video editing as well. Video files, especially raw and HD ones, take a good chunk of space in storage, so you want a sizable drive depending on how much footage you need to store. This issue can be alleviated if you have a preexisting storage solution, such as a NAS, file server, or sufficient cloud storage plan, in which case a 1 or 2 TB will suffice for data storage. I agree with the others about getting a SSD for the OS; it's much faster to load than the HDD.
Finally, case and power supply. For the case, get the same or larger form factor as the motherboard, so the board can fit in the box. Likewise, make sure the case is wide enough to have enough clearance for the cooler inside, especially if you got one of those big air-coolers. Other than making sure everything will fit inside, the choice in case is all about price and aesthetics. For the power supply, I absolutely agree with
kupu on this. This thing is the heart of your computer, providing electricity as your own pumps blood. Do
not skimp out and buy a "super cheap" PSU, as a poor quality one can fail early, potentially taking out other components with it. PSUs also have a form factor, which matches up with the case and board.
A DVD or Blu-Ray drive is 100% optional for a game recording machine, especially since Win10 and Linux can install from USB drives. However, since you do (plan to) have the software, you might in the future deign to record family-related recordings onto optical media, or make an instructional DVD for work, or some such. Plus, having the optical drive would be helpful if you buy software that comes in DVD rather than USB or digital download, or want to watch a DVD movie on your computer. A basic DVD RW drive should be reasonable in cost, if you desire.
One thing the others haven't mentioned:
When building the computer, take caution with regards to static electricity. Sensitive electronics + static electricity discharge = NOPE.
When you touch something, and feel the zap of ESD(electrostatic discharge, aka static electricity), you've unloaded 1,500 volts. If you hear the BZZT as well, that's 3,000 volts. If you can see the tiny lightning bolts, that's 6,000+ volts. However, components can fry from far, far fewer volts than humans can perceive, so you could damage one with ESD and not even know it. Those
usually-gray bags the parts come in when you buy them new? Those are anti-static bags, faraday cages that protect the components from ESD while they are closed with the parts inside. Leave the components in their bags until you're ready to install them, and save the bags if possible. You may also want a
grounding strap (example linked to show item and typical price range), and don't work on carpet.
When handling the components, don't touch the gold, especially with bare hands.
