What's important when ordering/buying my new computer ?
There are many things to consider when ordering a new PC. If it's going to be your main** computer, it has to be a desktop or (better) a 'tower' type with lots of room for hard disks (since, ideally, you want to start with least 3 identical hard drives) and enough memory for your chosen Operating System.
**A Laptop or Tablet is not a 'main computer', even if a Laptop/Tablet is what you use most of the time. As we will see later, laptops and tablets are essentially disposable devices that will, eventually, break down loosing everything they contain.
Unless you want a computer to play GAMES on (in which case you should be buying an XBox or a Wii), one thing you REALLY DON'T need to worry about these days is Graphics capability or CPU speed
How many cores ?
Some software - such as graphics and video processing software - can make real use of multiple cores (although more advanced software uses your Graphics Card GPU instead), in most cases multiple cores just means you can 'have more things running at the same time'.
So, whilst multi-core CPU's are 'better' (and every new computer comes with a multi-core CPU these days) you are not going to see much difference between a 2, 4, 6 or 8 core - where-as the difference between a 1.8GHz and 3.8GHz CPU (or 4Gb and 8Gb of RAM) is really noticeable. My recommendation would be 'go for the fastest speed' rather than 'go for the most cores'.
The problem is, that when it comes to actually running software, RAM access speeds can't keep up with CPU speeds - so 'the more CPU cache the better'.
Of course if you are processing image data, the cache won't help much (all that data has to be fetched from hard disk and/or RAM), so the '4 way interleaved' (Quad Channel) CPU's are your best choice (which means you must have 4 sticks of DDR3 RAM, or 2 sticks of dual-channel DDR4, see later)
This was once the preserve of the 'extreme gamer', however Intel now sell 'unlocked' chips and even Dell offer PC's with liquid cooling and overclocked CPU's.'Turbo boosting' has now entered the mainstream. However you should focus on the 'base' frequency of the chip. Turbo boost is all very well, but when it does 'kick in' the CPU heat dissipation leaps up and your cooling fan will switch from 'idle' mode to 'jet engine' mode :-)
When it comes to decent sound output, older PC's would drive a set of directly connected 5.1 / 7.1 surround sound speakers. However more and more 'consumer' PC's have HDMI 'built in' to the motherboard and these lack the direct connection sockets (the idea being that you 'pipe' your 5.1 to your HDMI connected 'Home Cinema' system instead of using a set of directly connected PC speakers)
Note that HDMI motherboard output depends on the CPU chip - the Xeon, i3 and older i5/i7 CPU's don't generate HDMI (aka 'Intel HD 530'), you need current generation i5/i7), so the motherboard socket will be 'mute'. Fortunately, even the cheap Graphics cards come with HDMI output, which will support 'surround sound' output (although you may have to search for how to 'enable' AC3 'pass through mode' if you want your Home Cinema system to drive your speakers). For older Home Cinema systems, getting AC3 out of your PC via S/PDIF will put you into direct conflict with the Music Industry and their 'DRM' restrictions, although if your motherboard supports S/PDIF (many 'gaming' PC's do, even if no socket is present on the backplate) and you dig around enough, it's usually possible to find a driver. Even some Laptops support S/PDIF (see below for Dell)