Make sure you pick the latest parts. The first and main component we'll look at is the Processor (CPU). The most expensive part. As of now, Intel makes the best ones out there. AMD can be a choice in the near future.
i3, i5 or an i7 the latest 6th generation Intel chip is super fast and very capable. Having an i3 with a decent Video Card will allow you to play almost any game on high video settings if that's the power you need. You can always spend the extra money and go for an i5; faster for single and multitasking processing power. i7 would be for a lot of multi-core usage. Prices go for $110,$210, and $320 respectively.
After picking a 6th generation CPU, we now know its socket type is LGA 1151. This means we need to look for an Intel Motherboard supporting that socket. Preferably the latest chipset which would be the Z170, H170, or Q170. I personally have been using Gigabyte motherboards for a while and it has proven great reliability and performance. A good priced one would currently be the GA-H170M-D3H for $90. If your budget allows you, the GA-Z170X-Gaming 6 would be a great option too.
Most users don't realize how much faster a computer would be with a Solid State Drive. A nice setup for every user would be a 120 GB SSD for the Operating System + Programs and another traditional Hard Disk (1TB goes for about $45). This will allow setting up scheduled backups to make sure all your data is always backed up. Note: SSD's are very cheap now.
A Memory module should be DDR4 with 2133 or 2400 MT/s. 4 GB or 8 GB would be a good start, you can always easily add more later.
You don't need to buy a Video card since now it comes integrated with the CPU, unless you plan on Gaming/Designing or Video Editing. There is a link that compares updated Graphics Card benchmarks. A decent one goes between $100 to $160. Depends on how heavy the system will be on the GPU (Graphical Processing Unit).
If you haven't picked up a Video Card a 400 Watt Power Supply would be good enough. Corsair, Antec and EVGA makes good priced power supplies. 600+ Watt would be if you have a video card. You can always Google search "PSU Calculator" and find out how much Watts will your System consume.
After Having the main components of a computer, you can now shop for a Case and CD-Drive. There are plenty of cases out there, just make sure you get the proper size, depending if you are going with a video card or not. ATX should be the size you are looking for.
Let us now if you have any questions.