Trophy,
As a landlord, you have landlord insurance. That covers fire and other catostrophic loses. It does not cover damage done by the tenants. In some areas you can get insurance that will repair vandalism, but I'd be surprised if you could get it in Buffalo because of the type of area it is.
As for lawsuits, the management carries insurance that covers themselves if they do something to get themselves sued. If they do something to get themselves sued, there is a good chance you will also be named in the lawsuit because they are your representative and acting in your name. It's assumed that anything they do with your property is with your blessing.
As the landlord, you have liability insurance included in your landlord policy. When you buy insurance, you carefully check to see what coverage is provided.
It's important to keep your property in good repair, so the tenants don't hurt themsleves on some unsafe feature of the property. There is a lot of difference between a lawsuit because the tenant tripped and fell and a lawsuit because their child fell through a rotted staiway banister. It's your job as the landlord to keep that banister safe enough that it will hold a person on the stairway and not dump them out into empty air.
You also must make certain that the insurance agent understands that the house is to be rented out. There is a huge difference between the policy for an owner-occupied home and the policy for a rented home. You don't want to buy the wrong policy and then discover that the insurance compnay won't pay becasue your policy doesn't actually cover you situation.
Insurance is very easy to buy: call 3-4 different companies, give them the address, and they will get back to you within a day with a price for the insurance and what the policy will cover. You must sign the application, but papers can be faxed, or sent overnight with Fedex.
If any real estate salesman told me I did not need insurance on a rental unit, I would find another agent. If they'd lie to me about the most important aspect, I'd wonder what else they'd lie to me about.
Note: many condo associations maintain "bricks and mortor" insurance on the buildings. That covers damage done to the building by fire, hgh winds, etc, and they usually have liability insurance for the common grounds. If you buy a condo to use as a rental. you still need to have liability insurance and insurance that covers damage to the inside of your unit.
The insurance is very easy to buy. It's not terribly expensive. If you do get sued, you call your agent and turn it over to their lawyers.