Hello Sarah,
Congratulations on on real estate wins. Having equity in a property is amazing for a number of reason. The one I'll focused on is directly related to your question of: "would I be able to get a traditional bank loan off the equity of my (future) duplex plus the equity from the single family home I have paid off or should I find another option for financing?"
It it very natural to associate bank with loans but I have learned in recent years that a Home Equity Line of Credit (HELOC) is more beneficial. One of the things I like most about the HELOC is the flexibility that it provides. Your HELOC provides you fast cash that can be used for any reason. Second think I about the HELOC is that as you pay down the principle, that amount becomes available for use. Take for example, you got approved for a $50,000 HELOC, you withdraw $20,000 to buy a property that you are going to renovate, you use an additional $15,000 for the renovation, total withdraw is $35000. Your After Repair Value (ARV) is $56,000 you refinance 80% of the $56,000=$44800. You then pay off the $35,000 balance on the HELOC and pocket $9800. Your credit line will be back at $50,000 and you just repeat the process.
**Number did not factor in closing cost and other fees.