Sounding a slightly contrary note to other posters... yeah, building your own PC isn't that hard, but there are drawbacks.
- Learning. People who've done the learning tend to forget how bewildering the avalanche of incompatible chip, motherboard and socket types can be - none of them with sensible, easily distinguished and memorable names. It's even possible to get confused about what graphics card you're getting, and how powerful it is. It can be a steep learning curve for those unfamiliar with this. It's worth learning, but it's not a trivial couple hours of reading and watching videos.
- Manual dexterity. Some people are just clumsy, or are dexterous but have very large hands. Some PC cases are just unfriendly to do a build into unless you have small fingers. Given you'd be handling components worth several hundred dollars, that may be something you're fine with, or you may not.
- Warranties. Building your own PC means that if any component goes wrong you have to remove that part, send it off for repair/replacement, wait for it to be returned, and then rebuild you PC. So you need to be confident you can diagnose the fault and identify the faulty part correctly. The warranty periods will be different for each part, so you'll need to be aware of which bits are still in warranty and which aren't. Having said that, failures are very uncommon.
- Cost. If you're careful and shop around, you can buy all the parts you need for less than the cost of a new machine - but not a lot less. If you goof, you can end up spending more, especially on new, high-end components.
鈥婩or your first PC, and for peace of mind, I'd suggest going to a reputable supplier of gaming PCs who do custom builds. Look at the specification for a $1,000 gaming machine, do a bit of research to get a feel for the parts they use, see if there are any you really don't need, and think about dropping those out and spending the money on having other parts better. You'll have a somewhat easier introduction to learning about the various parts, you'll get a fully tested machine delivered for little more than the price of a home built machine, and you'll very likely get a warranty which includes on-site servicing for a while, and at least collect-and-deliver servicing.
And, once you have a machine, you can ease into learning about the innards by doing a few part upgrades in a year or two. Then move onto a self-build when you really need to replace the whole thing.
If you were in the UK I'd suggest Scan's 3XS range. I'm afraid I'm not familiar with US customised PC builders.
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This 2014 poll for http://lifehacker.com/five-best-custom-pc-builders-1664766332 might help. And one more bit of advice - get the best PC you can afford. It may well be overkill for FO4, but some other game will come along, this year or next, that will need everything the PC has got.
Oh, and FO4 is quite likely to need a more powerful CPU than many other games, while not needing quite so much in the GPU department, but don't go crazy on the most expensive CPU you can find. A quad-core CPU with a high clock speed is usually better for gaming (for the foreseeable future) than an 8 core CPU with a lower clock speed. Most games don't exploit many cores well because hex and oct core PCs don't yet dominate the market.