Choose the Text tool and make sure nothing in your document is selected. Then, the rules of InDesign's Default Settings describe what happens: all attributes such as font, color, size, and paragraph and character style as well, that are "selected" at this point, will be used as defaults when you create a new text frame.
So, with nothing selected, just select the paragraph style you want to have for new frames. You will see that when you next draw out a text frame, it will have the correct style.
Be sure to check if you do not accidentally have a specific Object Style selected (both "Basic Text Frame" and "Basic Graphics Frame" ought to be good), as well as a specific Character Style other than "None".