I myself works as an insurance professional. Let me clarify one thing here. Your landlord will have their own insurance and you will have your own. There will be no overlap between the two policies as the landlord's policy will cover him and your policy will cover you. An example: If there is theft in your apartment and you loose your personal stuff, your landlord's policy has nothing to do with it. Similarly, if there is any damage to the elevator, storage area, lobby in your apartment building then you and your policy has nothing to do with it.
Your policy as a tenant will mainly cover you for the following:
1- Your personal contents (example: furniture, clothing, electronics and jewelry (check your company if they have a special limit for jewelry)
2- Additional Living Expenses: If there is loss/damage in your unit and you are unable to live in it for a short period and move out somewhere temporarily, then it will cover that expenses like hotels, temporary rental location etc.
3- Liability: If there is a loss to any person or any neighboring units because of your fault and they sues you for their damage then your liability coverage will protect you for that.
I am sure the above will clarify what is covered.
Please note that this is not a legal or official opinion and insurance rules/laws varies from province to province and with different companies.
With regards to the best company, visit
www.kanetix.ca because they deals with multiple insurance companies at the same time and they will connect you with the best company offering the best rate.