The single payment will cover both the original loan amount and the additional cash-out amount.HELOC might be better if you need intermittent access to funds, while a cash-out refinance could be more suitable for a one-time need with a clear purpose.

Or do the lenders require that I establish primary residence first, before getting an fha or a fannie mae loan for a primary? 

I understand that residential rental properties can provide positive incentives through loan paydown, tax incentives, cash flow, and appreciation.

For the previous 2 homes I own, I had my parents cosign the loan and that's how I got approval for each of loans, 1st primary residence in 2021 and 2nd in 2024.

With only a $50 or $100 origination fee, and "essentially" not losing any money to an interest rate, TSP loans are probably one of your cheaper loan options out there.I just took out a 40+k loan from my TSP to invest in other ventures and it was a very simple and straightforward process. 

@Nate SanowMy properties all have loans on them; LTV under 70%.  

The deposit is common in commercial loans.

For our previous investment properties we used a home equity loan and cash to buy and paid it off in a few years. 

All my tenants are students.

Is there anything that would prevent me from refinancing using a vacation home loan now?