Above information which you would provide to the bank in a loan application would be sufficient for them to decide under what conditions they would finance your project.

The minimum entry for a multifamily investment in Los Angeles may be in the $500,000 range.

I am going to be using an FHA 203K loan (if that's how you say it, still learning the lingo) and am looking for something in the 200-250 price range, or lower if possible but that might be hard to find in north Jersey.

If a property has been marketed to the public for a sufficient period of time, meets market conditions, what you paid IS the market value. 

You have to have some range for the agreement and it is a good idea to understand how a contractor  normally works to see how it works for you. 

For the same price range (up to 200k).

Despite our prices went down in 2008, they are already back up over 50% and turnkeys sell in weeks in most areas.I have seen some California investors purchasing SFRs rentals out of state in the $120k-$160k range, just to learn the seller, who was also an investor, had just purchased the house a few weeks prior for half price and, judging from the old online photos, the rehab was just paint and carpet.

With that 40+ another $10,000 or so of my own, I could theoretically pay cash for good deals as I find them in the $50-$60,000 range, then take out a collateralized loan on that new property and repeat.  

Right outside this will be a good sized game room with a fireplace, sitting area and sufficient space for pool table or other games.  

. , and using this money for the either down payment of 20% to purchase a $80,000 - $100,000 property that is an REO here in my area, which would give me a PITI of around $600 a month , and I can easily rent a property in this price range in my area for around $1,100 - $1,200 per month .... for a monthly cash flow of around $500 - $600 per month.I could then "Hopefully" do a No-Seasoning Cash-Out refi ( since I'll be purchasing the property as an Investor/Investment Property )....