@Sarah Auriemma your goal is to get started on REI path, by owning properties. I can think of couple of options in your situation.
1. As @Denis Ponder suggested, look into owning a duplex/triplex/fourplex and moving into one of the units. Downpayment comes from HELOC.
Advantage to this method:
a) This will become your primary residence and you'll get loan at lower interest rates (in current market).
b) Due to economies of scale, you can generate more rental income in future, not now. You have to sit tight for couple of years.
c) You can manage property yourself and keep the costs low.
d) Part of the mortgage is paid for by tenants.
Disadvantages:
a) The property you would be buying will be in higher range (>$500,000), which can add stress.
2) Since you own a ranch and if City Zoning laws allow converting your home from SFH to Duplex, you could do that and rent out the 2nd home.
Advantages:
a) Lower cost of owning a "2nd home"
b) Self managed, hence low cost.
c) Overall cost of project may be MUCH less than $350,000 required to buy 2nd house.
Disadvantages:
a) Well, there's another family on your ranch ... always.
NOTE: Whenever you take HELOC out, keep an eye out on interest rates. If you get variable rates, that can affect your calculations (and cash flow).
For more clarity, you should put your entire financials on a spreadsheet and model various choices you have.