And I suggest that you buy a dualtech detector, rather than a PIR, for a garage. There are too many living creatures that could give you false alarms.
This is also something to consider if you go down the wireless route - try to get a wireless pet-friendly detector. They're pretty rare - and you'll never get a wireless dualtech - but could significantly reduce the chances of false alarms.
Another option would be to fit a (battery backed) power supply to power a conventional dualtech and use its output to trigger a wireless transmitter back to the house. This could be a wireless door contact transmitter, for example.
As regards to the movement detectors even dueltech units are not immune to false alarms from insects moving over them, I use a twin beam infra red beam unit across the garage, contacts on the door and viper on the window with the led flashing to warn a would be intruder.
My car stays on the drive.