I don't use a LLC, just a personal umbrella insurance policy, and the taxes are done on Sch E.

What all points should I have to include in agreement with renters and property management company if I am able to do that contract through the LLC.LLC itself is on my name with an appointed manager who is near the property and will manage it.When I get insurance on the property, should it be business insurance as part of LLC or insurance with umbrella coverage, as property owner?

Lots of BP podcast episodes concluding that this sort of corporate veil is easily pierced and that you can use an umbrella insurance policy for greater protection than without it. 

Our buyer's agent when we bought the house was under the same big umbrella realtor firm.

For the properties I use Stessa - great to manage all your properties under 1 umbrella. 

I have two or three LLCs, each used as an umbrella to hold several rentals under.

Having said that, having the base liability insurance of $300-500k along with an umbrella of $1M seems more than sufficient.....assuming you’re not running some slumlord operation. 

It is currently under my name and I understand that is not safe method to go as an investor.I was wondering if umbrella insurance policy will be good enough to cover me if any tenant happened to "sue" or file legal claim?

Meena Price , of-course consult with your attorney and CPA but if your LLC does business in PA, it will need to be registered as a foreign Corp in PA and pay PA taxes.I don't see the benefit of of have a LLC registered outside PA unless you believe the business laws are much friendlier, which is why some people choose states like DE.Some people deal in their personal names and carry an umbrella policy for liability.If you ever want to get a mortgage from a bank, most will not lend to LLCs.

Once you get over $1M of net worth, you should shop around to find an umbrella policy.