Good day.I have one property with about $125k in equity.

In equity, it isn't doing anything for you.  

If I were to apply this method, would I have to pay PMI on the first home when it has less than 20% in equity in the property so I can apply the VA loan on a new property?

I have over 110k in equity in the property and want to use that money to jumpstart other rental investments.  

Therefore, under scenario #2, there would need to be at least $50K in equity appreciation over that same five year period.

So if you sell this property for $325k, of which $125k is your mortgage and $200k is equity, you must purchase one or more properties that have a total value of at least $325k AND you have to put at least that $200k in equity back into it.

I bought it as a bachelor pad 6 years ago, and now have around 25k in equity.  2/3rds of that has come from appreciation and the remainder from paying down principal. 

I do intend on buying a replacement property with a value of at least 4.8M , using $3.2M in equity, and replacing the debt at 1.6M, or, possibly adding more cash and reducing the debt load (possibly to $1M).

Houses that I'm looking at in NY are around $350k.I have a rental house in Texas with about 56k in equity that I bought using a VA loan.

Maybe not ideal, but positive cashflow and have a decent amount in equity.