1) Buy a good monitor
The monitor is the peripheral that you will interact with the most. For the sake of your eyesight and to prevent headaches from extended use, make sure that you purchase a quality monitor. Make sure that the monitor is the right size for you, don't be pressured into buying a larger monitor than you need. For most purposes a 17" screen will serve well. Also, read users reviews for the monitors even if you don't read reviews for anything else.
2) Hard-drive capacity
The more the merrier. Hard drive space is like cupboard space: you can never have enough of it, especially in these days of multimedia computing. The capacity of the hard-drive is more important than its speed. 100 gigabytes should be enough for most purposes, but if you know you are going to install many games, or store lots of movies or music files you may decide to buy a PC with a larger drive. Better to buy enough to begin with rather than buy a second drive later.
3) Build Quality
This is particularly important when selecting a laptop to buy. If you can, try and see the laptop models "in the flesh", check out the manner in which the monitor is attached to the rest of the laptop, and make sure the keys don't wobble around. The build quality is often the best indicator of how good a PC is overall.
4) Added extras
Make sure that you need all the added extras that come with the PC packages you are looking at. When it comes to additional software, decide whether you will be better off downloading and installing freeware virus checkers etc. Sometimes the additional virus checker only includes one years worth of updates.
Decide whether you really need the packaged hardware. Would you prefer to buy a printer separatelty? When it comes to printers check how much new ink cartridges cost, as you may end up with a printer bundled with your PC that will cost more in ink than buying a separate printer which uses cheaper ink cartridges
5) Power Supply
Find out what wattage the PC's power supply is. Again, this is a case of the more the merrier. I have known some PC manufacturers to install power supplies that are barely adequate to power the PC, let alone any additional cards you put in it later. Avoid anything less than 240 watts output. It may be difficult to find out the power output if you are purchasing online as it is rarely included in specifications, however, you could email the manufacturers who should be more than happy to respond (if they think there is a likely sale).