The size of the HD used for Time Machine is important but is not a deal breaker.
The larger the drive, the more backup information you can store on it.
Time Machine works by backing up the entire contents of your hard drive. You do not pick and choose what files to backup, you get the whole lot.
That said, you have to have room on your Time Machine drive to accommodate all that data. Each time that TM backs up, it does it every hour, it performs an incremental backup, only copying those things that have changed.
A good rule of thumb would be to find out how much data you have on your hard drive, Select the drive/Get Info/Used, double it and get a drive of that capacity, at least. I would not go with anything lower than 200GB.
As TM moves along, and the drive becomes full, it will automatically delete the oldest files to make room for new ones.
As an aside, your new external drive should be initialized before you first use it. Although "most" drives will work as soon as you plug them in, this is because they are formatted as FAT or FAT32, you need a drive that is specifically for the Mac. Format the drive into 1 partition, HFS+(journaled) and as GUID for an Intel Mac or APPLE for a PPC Mac. (Disk Utility/Partition/Options) A drive that is formatted APPLE cannot boot an Intel Mac.
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How should one size the external disc used by Time Machine? In its recent release of Time Capsule, Apple offers external discs of 500GB and 1TB. 500GB is certainly enough for my application. Is there any way I can determine if I can use a smaller capacity drive?
Thanks.

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