What is Father Ted's car from the TV show?

It depends which episode.

In the episode "Good luck with the book", the car he was in when he rear-ended another car at the traffic lights and got punched in the face was a MK III Ford Escort.

In the episode where he tries to hammer out a small dent but goes to far and ends up wrecking the whole car, the car in question is a Rover 213.

In the episode where Father Jack nicks Ted's car and drives it around recklessly, the blue car in question is a MK IV Ford Cortina.

There may be other episodes involving other cars but these are the most obvious examples that spring to mind.