Most schools have part timers to meet the weekend busy periods.
The school I work at has lots of them.
I started instructing full time about 2 mths ago, but have gone back to IT contract work for 3 mths to avoid the bleakness of winter. Apart from the money, I know where I would rather be.
You won't need to start full time before going part time, however the weekend guys usually have less interest in airline jobs and therefore do not tend to "move on" thus not freeing up an employment opportunity.
Students first do trial lessons and usually stick with the same instructor if they decide to do their PPL's. A lot of these will only do weekends so eventually you will have lots of students.
Good luck.
FIS