Furniture garbage..

Hey, I'm new to this forum in the sense of posting. I'm living with my parents. Our home is under renovation. Currently, furniture works are going on, mainly cutting and polishing. So daily we need to clean the house before going to bed. More than cleaning, waste disposal has become a headache!
As you know, in a city like Toronto, DIY waste management is a difficult task! Besides, we forced to spend more on this waste disposal even after cleaning on our own!!!! So I'm planning to rent garbage bins to resolve this issue. I've gone through their site for more clarification. I found they are providing huge bins concerning the large sized garbage(that is what we want now, sometimes we have larger furniture parts to dispose of).
I don't have any prior experience in hiring such a service, but I heard there would be incentives while disposing of older belongings, that we're no longer using. Is that true? If so I'll be fine, because we have old furniture here, which we need to remove soon.