Seeing that the only way to get on top of the mountain is by using the Teleferico you may want to consider cheaper options when visiting the Cristo Redentor (ex. hiking).
The view you get of the city is, to say the least, incredible. You'll want to spend 15-20 minutes on the first mountain and a bit more once you're at the very top.
Best times to go:
- early in the morning to avoid crowds
- before sunset in order to see it
Suggestion: go to Praia Vermelha - right below it - during the day and then go up to see the sunset.