If you do not have substantial assets for someone to come after in a lawsuit, then having liability coverage is sufficient. 

One of my concern was, if one of the lender doesn't accept at the time of underwriting , I may not have sufficient time to work with next one.

This is normally a game of quantity.  

If there is sufficient equity, try to make a deal.

The power of leveraging allows the first time buyer as little as 3.5% cash in the FHA version, but with adequate credit and sufficient down payment, the FannieMae Home-style opens the door for less or no mortgage insurance AND is available to the investor.

When a property is described you usually have a property that is either Stabilized (meaning up and running efficiently, fully leased or close to, basically retail ready condition), you have Value Add (minimal deferred maintenance, operational inefficiencies or capitalization problems or other issues which allow the property to be run sufficiently better) and finally Rehabilitation Condition (needs a lot of repairs, not currently rentable, etc).Value Add Condition properties are more about the new operator coming in and turning it around from a management standpoint and much less about taking a run-down structure and repairing it.

For example:$69,000 property with 4 unitsGross income at ~$1,40030 year mortgage with 25% down ~$250I'm trying to decide between quality and quantity.    

He might not always be low bid, but the extra dollars spent for quality, quantity and trustworthiness are well  worth it.

Or, is the structure "institutionalized" with sufficient capabilities to back up key positions?

I would also want to budget 6% for Cap Ex.I hope I answered all your questions sufficiently.