UK logos reach us as email-signature JPGs, low-resolution PNGs from an old website, or a photo of a signwritten van. All of those work, because we don't push the image through converter software: a digitiser rebuilds each part of the logo as stitches.
Rebuilding lets us sharpen soft edges, fix wording that has blurred, and choose satin, fill or running stitch for each element. Automatic converters skip those decisions, which is why their files often look fine on screen and then pucker on a polo. The DIY routes are explained on converting an image to an embroidery file.
Caps need their own build: see the cap version of your logo. For print, signage or vinyl you need vector artwork: see vector conversion for print.
Putting one logo across a whole staff uniform? See corporate uniform sets or workwear digitising.