To answer your question about what to look for, the 2 MAIN things that affect PC / laptop performance are:
1) Processor (this is the CPU, usually made by Intel or AMD. You may see names like Pentium, Dual Core or Athlon etc)
2) Amount of RAM (also known as Memory).
Obviously the faster the processor and the more memory the better the PC will go.
Almost all processors made nowadays will be fast enough for basic internet, word processing etc. Unless you plan to play games or do video editing then dont worry too much about the actual processor.
The CPU speed is measured in Ghz (giga hertz) but Intel and AMD dont measure their CPUs the same way so that does not always tell you what is fastest.
Memory comes in various sizes and nowadays most computers come with either 512Mb or 1024Mb (1Gb).
Some come with 2048 (2Gb) but that is fairly rare.
A PC with 512Mb is about OK (dont buy one with less), and 1Gb about perfect. You are not likely to get 2Gb unless you pay a lot for the PC.
There are loads of other numbers related to a PC but you can probably ignore most of them.
Probably the other two most important things are hard disk size (try to get 80Gb or more) and screen / monitor size (try to get 15.4" on a laptop or 17" or more on a PC).
Neither affect performance but are nice to have.
Try to get one with a CD or DVD writer as you will need to back up your personal files in case the PC crashes or gets lost or stolen.
Good luck