If its not someone you know the lender will dictate the terms.

If you're considering hard money loans, they can provide fast funding, but with higher interest rates and shorter terms.

What terms are they proposing?  

I've also used traditional loans through regional banks and a few SBA loans. 

Would a HELOC or home equity loan on my personal home be a good idea to fund this?  

I'd rather keep the sub-3% rate for now and finance other properties conventionally for the short term.

You said that you are applying for an FHA loan so it sounds as though you'd be living in one unit. 

Financing OptionsParent Loan Options: Consider home equity loans, investment property mortgages, or co-signing a loan.Tax Implications: Speak with a financial advisor about potential deductions and capital gains.Rental Income Potential: Explore the option of renting out extra rooms to offset costs.5.

You can allocate those proceeds any way you want - as equal down payments or buy one for cash and others with loans - It doesn't matter a bit as long as you use all of the cash and purchase at least as much as you sell. 

Much better as a short term acquisition strategy for flips IMO but always a high-risk strategy that should not be practiced by anyone who doesn't have the liquid capital to pay off the loan if needed.