More and more frequently I'm getting the running out of hard disk space message... just need some input as to what type of external device I should invest in. And should I use Time Machine along with the external drive? I've yet to face this situation, and need to do something quickly... I work at home using both my laptops and can't afford for this MBA to die on me!!!
First, YES YES YES you should be using Time Machine to back up both your internal and any important external drives, unless you have a different backup strategy (such as Carbon Copy or maybe an online service such as Carbonite). Just have a backup strategy. Time Machine is quite good. Do see my note further on about configuring Time Machine to back up the external drive, though. By default, it will ignore the external drive.
First, rather than going external, you might consider upgrading your internal hard disk to a more capacious model. If your machine is more than eighteen months or two years old, the drive may be getting close to the end of its lifespan anyway. It really is not difficult to change them out; at worse there will just be a bunch of teensy screws to deal with and, for pre-unibody units, some moderately annoying separation of the palm-rest from the body using a soft (non-snappable) plastic picnic knife ("spudger") or somesuch. If you're reasonably handy it is no big deal and will take you less than an hour. If you choose this route, start by backing your machine up with Time Machine. Then power everything down and carefully swap the hard disk for a compatible bigger unit using instructions from ifixit.com. Then, format the drive using your Snow Leopard CD and restore your machine via Time Machine. Voila: more space, and your machine will be exactly as it was. (Pick a drive with a higher spin-rate while you're at it.)
If you go external, consider your planned usage of the external drive. If it's mostly for storage, any old USB drive will be fine. Bus-powered units are preferable to those requiring AC power. You can get good ones (such as the Western Digital Passports) for cheap at Costco etc. But if your usage will involve frequent usage and continuous I/O, such as when running a virtual machine from the external drive, then a drive with a FireWire interface will give you snappier performance. They cost a little more. The only issue to be aware of is that Mac laptops have crappy FireWire ports that don't snap securely, so connectors are easily dislodged. So you must be careful-- you can trash a drive if it disconnects at the wrong moment.
Whatever you do, remember that the external drive needs to be backed up too. Time Machine will do that, but note that external drives are excluded from TM backups by default. You have to click the Options button to un-exclude it, then it will be backed up along with your internal disk. Note you'll need a backup drive at least twice as big as the combined size of the internal and external disks if you do this.
My work involves having ready access to dozens of virtual machines of various configurations. Ergo: I use an external FireWire drive, a nice Western Digital unit, very pretty. Mobility is important for me, so I have a big stripe of ~50mm wide fuzzy black Velcro running across the back of my MacBook Pro about 35mm from the hinge. Doesn't look too bad. My external drive has a corresponding piece of mating Velcro on it so it may be securely attached. It's a lovely solution... but mind that FireWire cable! Easily dislodged on the Mac side. Before I found this FireWire drive, I used a USB Passport, and that worked acceptably, but the FireWire drive is perceptibly snappier.
One final tip. You might consider why your disk is running out of space. There may be some things you can do. For example, virtual machines can be configured to span multiple files of smallish size so they gradually expand to their maximum size with usage, rather than taking up the entire lump right from the start. Similarly, if you routinely utilize disk images for storage (perhaps for security, as they are readily created and encrypted using Disk Utility), use the sparsebundle type, which again are chunked into multiple smallish files that gradually expand with usage rather than taking up their designated amount of space all-at-once. ...These tricks benefit both your available disk space on any given day, and they also really impact your backups since only the smallish files that have changed need to be backed up rather than one great big file that contains perhaps only minor changes.