Apple External Drives
How big should my Time Machine backup drive be?
Understand that Time Machine takes a snapshot of your whole system and stores it in the backup drive. Say, for example, only about 120GB of your internal HDD is in use. Then it'll only take a snapshot that's about 120GB in size, and while that same snapshot will grow over time as you take more recent snapshots of your system, it will never go beyond the maximum size of your internal HDD.
A general "rule of thumb" is, to keep a reasonable "depth" of backups, Time Machine needs 2 to 4 times as much space as the data it's backing-up (not necessarily the entire size of your internal HD).
Be sure to add the size of the data on any other drives/partitions you want to back up.
And, of course, the larger the drive, the more old backups Time Machine can keep for you. A drive that's too small may only have room for a few weeks (or even days) of backups.
Unfortunately, it's rather hard to predict, and most of us have a tendency to add more and more data to our systems over time, so if in doubt, get a bigger one than you think you need now.