This summer, I put together a write-up on a PC I built for photo editing and software development. That article has been really helpful any number of times in documenting what I put together, but after a few months of living with this build and explaining why I chose each of the components, I think it might be worth a follow-up to broaden the discussion a bit.
With that in mind, here's some additional commentary on some of the more important components, along with an explanation of what you might want to look for (and why) if you want to build your own PC. Given the rate of change in PC components, timing is important -- we're just now approaching the big holiday sales in the fall of 2013, so bear that in mind if you look at parts or prices later.
This is as good a place to start as any. Recall that I chose the Fractal Design Define R4 Case – Black, and I love it. Very clean-looking, without any neon lights or alien spaceship designs, and it's designed to be very quiet, too. Depending on your needs, though, this case might be overkill -- it's pretty large, for instance, so unless you need all that space, another case might be better. I like this Fractal well enough that I'd consider another case from them, and I've had good experiences with Antec cases in the past. This is really one area where you can largely choose what you want based on aesthetics. Most cases will give you plenty of functionality for a basic build, and if you've got specialized needs (lots of room for HDDs, big video cards, or water cooling) you probably know what you're looking for already.
If you're upgrading an old PC, you might very well be able to use the same case, as long as you're happy with it, and if you intend to keep building your own PC's for a while, buy a case you like, because it might be the longest-lived PC component you buy.
I got a Seasonic SS-750AM Power Supply, and I've had zero problems with it. Again, it's likely you could get away with something smaller, say, in the 500-600 watt range. A modular or semi-modular power supply is nice because at least some of the internal cables can detach from the power supply if you're not using them all (which is very likely). This will help keep your build a little more neat & tidy. The other big feature to watch for is an efficiency certification -- "80 Plus Bronze", for instance. This is an indication that the power supply runs efficiently, which is, itself obviously a good thing, but it also tends to correlate to quality because the power supply must be built reasonably well in order to pass certification.
Good brands here include Seasonic, Corsair, OCZ, Antex, Cooler Master, and Thermaltake, but be sure to read reviews, because all of these brands have some good units and some that aren't quite as well-received. In general, companies that specialize in power supplies (or have relatively narrow product lines) tend to make a better product -- they have to, because their eggs are in fewer baskets. Seasonic is one of those companies. Plan on a price between $70 and $100.
Motherboard / CPU
I'm going to talk about these together, because of all the components here, these two are absolutely tied to one another. The first thing you need to decide is whether you're going to use an AMD or Intel processor. Choose Intel. AMD makes a good product, too, and you can probably save a few bucks if you know what you're looking for, but if you don't know exactly what sort of AMD you'd buy, and why, Intel is easy and reliable.
Next, decide how fast you want to go -- if you're using Intel, you're looking at some variation of Core i3, i5, or i7 processor. The current generation of these CPU's is known as "Haswell". These are minor improvements over the last-generation "Ivy Bridge" processors for desktop applications, though they bring big power savings that make them very attractive for portables. For this reason, if you find a good deal on an Ivy Bridge processor, don't hesitate to pick it up, though all things being equal, you'd prefer the newer Haswell on an apples-to-apples basis. Intel part numbers can be a little confusing (you'll see a four-digit number), but it's not too hard to understand the code: the first digit is the generation, so "4000" processors are Haswell, and "3000" processors are Ivy Bridge. The second digit corresponds roughly to class -- "3" is a Core i3, "5" or "6" is a Core i5, and "7" is a Core i7 processor. For most users, a Core i5 or even i3 will be just fine; only the most demanding users will benefit more from a Core i7 (vs. upgrading something else in the system, for instance).
One thing to pay attention to, if you're going to use Intel's integrated graphics, is that different processors have different graphics capabilities. This chart, while a little overwhelming, contains all the info on cores, clock speed, graphics, and so on for Haswell processors in one place -- it's a pretty good reference for figuring out where in the lineup you want to be.
In general, RAM is one of the most cost-effective ways to boost your system's speed. Don't cheap out here -- I wouldn't build a system with less than 8GB of RAM today, and if you're going to do anything to stress the system at all, I'd spec 16GB or more. For most people, any DDR 1600 RAM will be fine - you don't need the super-clocked stuff unless you know what to do with it. You'll buy RAM in pairs, generally -- in my case, I bought two 8GB sticks, giving me 16GB of RAM with two slots left open to add more later, should I desire.
Pay attention here - disk drives are one of the most important parts of your system, and if you choose your setup wisely here, it can pay big dividends. The normal practice here is to grab a single hard disk drive (HDD) and drop it into your system and be done with it, but you're missing out on a couple of big improvements. First, a conventional HDD is relatively slow by modern standards, though it offers a ton of storage at a very low cost. A solid state disk (SSD) drive, on the other hand, is lightning-fast, but fairly pricy on a per-unit basis. The solution? Use both. Get a SSD to use for Windows and your program files, and use a conventional HDD to store all your data. Make sure it's a SATA-3 drive, and look for a capacity between 100GB and 256GB or so.
Next, all modern motherboards will give you the opportunity to set up two HDD's as a mirrored pair, so that anything that's written to one winds up written to both. This way, when one of these drives dies (and it will), the other keeps right on chugging, giving you time to replace the other half of the pair without losing any data at all. This is known as RAID-1, and even though it's not a substitute for real backups on an external medium of some sort, it's been a life saver for me on multiple occasions. I can't recommend it strongly enough. Don't forget to back up your SSD, too, by the way - even though they have no moving parts, they do fail, and you don't really want to get caught without a backup!
Hard drives might be another area where you can migrate parts from a previous build as long as you're happy with their performance.
The first option for you for a video card might just be no video card at all. Most modern motherboard and Intel CPU's have built-in graphics processors that are pretty passable for 2D and light 3D needs. Unless you're gaming of doing photo or video processing that you know takes advantage of a Graphics Processing Unit (GPU), it's very possible you won't need a video card at all.
If you decide you want one, though, video cards (and brands) work a little differently than most other components. There are two major video chip vendors: NVidia and AMD. No matter what brand of card you buy, it's very likely it'll have a chip from one of these vendors in it. In fact, there's not a lot of difference between a card from EVGA vs. MSI vs. anyone else as long as they use the same chip and video RAM. The various manufacturers differentiate themselves by boosting clock speeds slightly or by building cooler-looking heat sinks and fans. Still, sticking to a reputable vendor like EVGA, MSI, Gigabyte or Asus is probably a good idea unless you've done your research.
These days, it's possible to build a new PC without an optical drive by booting off a USB stick, and we certainly don't seem to need an optical drive as much as we used to, so I actually attempted to get by without an optical drive for a while. After six months or so, though, it turned out to be more of a pain than it was worth. A basic DVD reader / writer is no more than $20 or so these days, so pick one up or migrate one from a previous build.
Don't forget that you're going to have to put an OS on this machine. If you've still got installation media from your other applications, you'll probably be able to move those to a new PC, but Windows can be a little touchy about this. Microsoft's licensing policies are notoriously complicated, but recent consumers packaging comes in two flavors: Full retail, which you might be able to move / reinstall, and OEM, which is tied to one PC forever (so you can't migrate it). Pick your poison on this one, but don't forget about it when planning your build.