It seems like choosing an external hard drive would be little more than a question of price. But this is far from the case. There are a number of important considerations one needs to take into account when choosing an external hard drive.
1) Purpose - The answer to "why do I need an external hard drive" is going to drive the rest of the considerations when choosing a drive. If it's just to store your documents and work or school stuff, then you probably don't need a very large or very fast drive. On the other hand if you are planning on using it for media projects you speed and capacity are important things to think about.
2) Capacity - Most external hard drives range from 500 to 2000 Gb these days. The more space you want, the larger and heavier the drive will be.
3) Connection - The choices here are USB and Firewire. USB will work just fine for a PC or casual use on a Mac, but if you intend to do any sort of media work at all you need a Firewire connection. This will make file transfer much faster. Some external hard drives actually come with both Firewire and USB connections. You should know that Firewire connections are much more common on Macs than on PCs.
4) Format - When you buy an external hard drive it will be formatted for either Mac or PC. It is important you purchase a drive with the format of the system you plan to use most often. While, depending on the format, one may work on the other system, problems can and do occur with cross-use. Be warned.