Well if all you do is browse the internet with occasional funny cat video from youtube about any cheap desktop may do. You can even save a lot more at that point and get something like a Raspberry Pi lol, smaller than smart phone and can act like a computer to a point for about $30
Now, if you want for things to run smoothly, more intense application to perform faster you should start to care about what parts are there. I usually build my PC myself and spend around $1200-1600 on them. You can easily spend more, but I do not find that I can spend much less than $1000 and still get decent components.
Websites such as
http://www.cyberpowerpc.com will build PC for you from whatever parts you want if you do not want to put it together yourself. Of course for that you are paying a bit extra.
To check how badly you are being ripped off by companies that build computer for you,
http://pcpartpicker.com/ can be used. there you can find any component and put it into the proposed system. It searches over couple of websites to find you best prices. Once on website go to System Build button up top and start filling things in.
http://www.tomshardware.com/forum/forum-31.html Has a number of topics with polls for best PC for different applications, you can use those as a jumping off point.
As far as various parts (I do not know how much you know so this may be obvious):
CPU - This is what does most of the computation on your computer for most of the tasks. I would recommend staying with one of the Intel CPUs instead of AMD. As far as model choose i5 or i7 (both are in YXXX[k] format - Y shows generation, stick with 4, if k at the end is present that mean this CPU can be overclocked easily, you might not care for this part). Difference between i5 and i7 is numbers of fake number of cores. Basically CPUs are not built as a single big unit anymore, instead they stick few smaller CPU together on the same chip. Both i5 and i7 have 4 of these CPUs crammed in the same chip. But i7 has a hyperthreading technology that makes it a bit easier to switch between two applications, virtually giving you double the amount of cores. So your computer will actually thing you have 8 cores instead of 4 that you physically have.
Which you want will depend on the application - if you run a lot of programs at the same time i7 may be useful, otherwise it actually is more beneficial to stay with i5 model.
Memory - Scratch paper that your CPU uses while programs run. Higher amount is basically better, you are likely be good to go with 8gigs of this, going higher will not likely benefit you. Memory also has speed associated with it, here you can just stick with 1600MHz versions. For a brand I prefer Corsair.
Motherboard - everything plugs in here, it does have some other processing units. These can range from $70 to $300, higher priced MBs will include more things such as WiFi cards, bluetooth, etc. which might not be all that useful on a desktop. But they will also include better quality capacitors etc. Main parameter that is always included with MB is the chipset, latest one is Z97, I would suggest you get this. For a brand I always go with ASUS.
Hard drive - Basic storage. You may want to consider at least one SSD drive where all you programs and operating system will be installed. These are much faster than normal HDD ones. Size of 128g for the primary drive will give you plenty of room for Windows and bunch of programs. Secondary drive would then be just used for storage of say video and pictures, here you do not care as much about fast access so normal HDD drive would do. I would still look for a drive with 7200RMP, this affects how fast data is read. Size depends on your needs. 2 TB should be a good start.
For SSD something like Samsung Evo 840/850 would be a good choice. For HDD Western Digital Black, Blue, or Green (Black are faster drives, then it's Blue and then Green).
Video Card - Your motherboard will come with some basic video card capabilities. You are likely to benefit from having an actual video card for things like video editing as some of those calculations can be done by the video card instead of the CPU. Here I prefer nVidia cards and I usually go with ASUS for the manufacturer, although most brands should work as they all follow nVidia's specs when building the card. GeForce 970 that recently came out is a very powerful card at a very good price so a very good value, of course you may not need this much, but it would allow you to play games if you ever want to at very high quality. Other wise look at something in a previous generation 7xx, I would probably stay at 750+ model numbers.
Power supply - for what I've described so far 500-600 watt range would do. You may want to pay attention to the ratings of the PS such as Bronze Silver Gold etc. That shows how efficient they are and how clean of a power they produce. Good brand names here are Corsair and Seasonic. Getting a higher watt PS is ok, that will not mean that your PC always draws that many watts, just that the PS can supply that many if needed.
Case - Mid or Full tower would be a good choice, unless you have to have a very small case. Usually whatever is selected by default when you build a PC on some website should be ok. But more hole/fans, bigger size may be better for better cooling of components.
Sound card - Whatever is on the motherboard should be ok for this. On higher end MBs you may even have a rather good built in sound processor that would beat most of the cheaper sound cards.
Misc - blue ray drives, card readers, keyboard, mouse etc. add what you need.
