For smaller, portable external harddrives we have a Smartdisk FireLite (named Rodney). It ha worked excellently for years. For backups via Time machine with 500 gig storage we hav an Iomega which is built and designed for the express purpose of sitting with a mac mini and being its backup. (They are the same size and shape and color.) It's name is Radek and again, it works extremely well and we are very happy with them both.
ETA: I thought someone would have answered this, but apparently not. ;-) Firewire is the type of connection. For example, you have a USB cord which you can plug things together with. "Firewire" is another way and it is much faster than USB. So for backups, high volume transfer, etc, FireWire is better. You must have a FireWire port (plug in) on your machine to use a FireWire cable. Some external harddrives have FireWire, some do not. Mac backups recommend using FireWire as otherwise it kinda takes all night...
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ETA: I thought someone would have answered this, but apparently not. ;-) Firewire is the type of connection. For example, you have a USB cord which you can plug things together with. "Firewire" is another way and it is much faster than USB. So for backups, high volume transfer, etc, FireWire is better. You must have a FireWire port (plug in) on your machine to use a FireWire cable. Some external harddrives have FireWire, some do not. Mac backups recommend using FireWire as otherwise it kinda takes all night...