The Apple technicians told me that I needed a specific device to use Time Machine... namely a wireless device that had a relatively small hard drive.
Since I use Oracle Virtual Box and have very large files, I think it would be best to backup using Thunderbolt, instead of Wifi.
Can I use a normal Thunderbolt harddrive and have Time Machine work with that?
Yes. You can use Time Machine with any directly attached hard drive. It is much faster, although if you have a laptop, it is somewhat less convenient to remember to plug the drive in than to use wireless.
The folks from Apple were probably recommending a Time Capsule, which is a wireless router with a built-in drive for backups. It's definitely an easy way to do it, but not required.
As per Alan's answer, any drive will do. It's your call as to how big it is, and how fast the access to it is etc.
A point of note though, is that by default Time Machine works on a per file basis (at present), not a block basis, and as such those who use data that is held in single large files that regularly change, will find that TM regularly shifts a lot of data to their backup drive. This can result in filling your backup drive quickly, constantly backup etc etc, and you may find that there is a better solution for certain files like these.
For example, Entourage stores all it's mail in a large database file. Receive one email, and the whole database is backed up again. Make any change whatsoever to a virtual machine file, and the whole file is backed up again, every hour. The other day I was just using Twitter for an hour, and it backed up 14Gb. I couldn't understand why as I hadn't used any other program, until I realised I has Steam running, and it has downloaded a couple of updates...
If your VM program of choice has the ability to make snapshot backups, you may be better off making a manual copy of your VM files to your TM disk (You can arbitrarily store data of your choice on the same drive as your TM backups, just don't use the TM folder structure), then exclude the file from future TM backups, and set up regular snapshots instead, backing those up. Other workarounds exists I'm sure.
Of course, if your data is important to you, you should do whatever it takes to back it up, and a Thunderbolt drive will handle it I'm sure, just make sure that you have a seriously large drive attached to ensure that it's not filled too quickly! If you have say 100Gb of VM machines, and you use them all during a 7 hour working day, you could in theory push out 700Gb of backups per day, which Thunderbolt will certainly handle, but even if you have a 2Tb drive hanging off the wire, you won't even get 3 days worth of backups before it's full and starts replacing the earlier ones. And that's not a very good backup regime if your data is important, in fact it's barely any better than a once a day drive clone.
Just some things for you to consider :)
