In the US having a paid for property does not hurt your chances on getting a loan on that property. In fact many options are available to you in that case. First you can get a traditional mortgage on the property and should stick to 80% of appraised value to avoid PMI. With a traditional mortgage expect to pay about 5k or so in closing costs.
Second you can get a Home equity line of credit, which was outlined in D Stanley's answer. These typically have a variable interest rate which is not attractive.
Third, some banks offer a fixed rate home equity loan. They can offer no closing costs, and do a fixed rate for a fixed term. Traditionally these are done in 7 or 10 year time periods so the interest rates tend to beat traditional mortgages.
As D Stanely said, it is not a good idea to put your home at risk for a business idea/opportunity. How much experience do you have in the rental market? How much cash do you have, besides this money, do you have to pay for the eventual mistakes you will make? How much do you plan on setting up a proper organization for the business? Are you even properly evaluating these properties?
I feel like you cannot come up with good answers to those questions and it may very well lead to losing your paid for home.
However, if you decide to move forward, please make sure you set up your business properly. Talk to an accountant or lawyer to setup a company to buy these properties. Do this before actually buying the properties.
Hopefully you have the income to support the mortgage if these investments do not pay out as you plan.