Hi Little Dawgy - not sure that dogs take advice from cats too readily - but here goes ....
Firstly, have you considered simply bunging in a new (bigger) hard drive, either as a replacement, or as an additional drive? You don't specify the size of the hard drive that is rapidly running out of space, but I make my systems last a bit longer by simply doubling the size of the installed hard drive every twelve months - that way I get about three years out of them.
Plugging in a USB drive does have benefits (it's relatively painless as long as you're using an OS later than Win 98, and it makes your data very portable, and very secure too if you take the trouble to lock the USB drive away in a safe place). But -- be aware of a couple of the downsides: Firstly, it's quite slow, particularly if you are shifting large amounts of data. I haven't really kept a record of times, but moving 20 - 30Gb of data took several hours (and that was using the the faster USB 2.0 port). It gets even worse if you want to do somethinh eccentric like a complete ScanDisk - that took 28 hours on a 40Gb drive, albeit running it on my laptop (266Mhz Dell with 196Mb memory). Couldn't afford to tie up my desktop machine for that amount of time.
Secondly, be aware that not all USB ports are created equal - in my experience, trying to plug a previously installed drive into another USB port can create significant hassles, particularly if you have a number of USB drivers installed (for example, for memory sticks). All these devices seem to use a different driver, and trying to sort them out can be quite a nightmare (on Win 2000 at any rate - Win ME might handle things better). I have "lost" my CF + SM card reader - the system sees the device, but the drive letters never appear in Windows Explorer (I'll get around to sorting that out "Real Soon Now").
Thirdly, be aware that a USB device can only be seen by Windows - in other words, you cannot use it as a back up device for programmes that need to see a DOS device (for example, Symantec Ghost cannot write to a USB device because it can't see it.
You can either buy a complete enclosure + drive (for example, the Western Digital 120Gb Combo HDD), or you can buy an enclosure and then put your own choice of drive into it (cheaper but somewhat more hassle to get the jumpering right). I am using a Chronos Mobile Disk enclosure with Western Digital 40Gb 3.5" drive - works for me! This has an external power supply which is a bit of a nuisance - I probably should have gone for a Tsunami Deva Mobile Storage which is a bit bigger but has an internal 42,5W power supply built in. I think I would be a bit cautious of the 2,5" disk enclosures which run off the power from the USB port - these may not work off a USB hub unless it has a power supply, and will be quite expensive for the capacity you are looking for.
Hope that helps - Miaouw! (How did I manage to beat Richard on this one? Maybe he's off flying!)