I’ve been in the same situation, and the results from free tools were never great. If you want your design to look professional when embroidered, you really need proper digitizing. I recommend using Digit-It — they do excellent logo embroidery digitizing and can convert your design into the right machine format.
I’ve used them for custom patches embroidered and custom made embroidered patches, and the stitch quality came out perfect with all the details intact. Their turnaround is fast, and it saves you the headache of trying to get it right yourself.
If you still want to try software, Wilcom and Hatch are popular options, but outsourcing is usually much faster and gives professional results. https://www.shop.digit-it.com/