If you are completing 2 math units in first year (Calc 1/Calc2 or Calc2/Linear or Accelerated 1 and 2), you can apply at the end of the year (I'm pretty sure it's recommended you apply at the end of the year).
If you are not doing 2 maths in first year, it's advised that you apply at the start of the year so you can sort out your course with a mathematics course advisor or something.
In terms of which maths would be best for engineering, I'm going to have to say Applied Mathematics. I'm not 'too' sure about the others (definitely not pure maths) because stochastic processes are used in telecom engineering (electrical speciality) and discrete mathematics is used in computer science / software engineering. However, since applied mathematics deals with differential equations and the such, I reckon it'll probably be the best specialization for your situation.