I recently bought one of these (
http://www.aliexpress.com/item/GT02-GPS ... 60442.html) for ~US$40 shipped to NZ. The documentation is poor, but there's a pretty good discussion on Dealextreme (
http://club.dx.com/forums/Forums.dx/threadid.1130935) including how to configure it for online/web-based tracking.
Haven't installed it in the Mini yet (contemplating whether to put it under dash or in the boot somewhere - depends on what interferes least with the GPS signal), but have installed a SIM card and tested it thoroughly - works very well and you can receive location via text, or set up timed monitoring via a web-based tracking site.
The only downside to this specific device is that it doesn't have an on-board battery, so potentially may drain the battery if the car isn't used for a while. It is, however, probably the cheapest option available.