Digitizing is not converting. A logo file holds colours and outlines; an embroidery file holds an ordered list of needle points. Nothing in the picture says which areas are satin, which way a fill should run, or what should sew first. That is the work, and doing it in this order keeps it short.
Everything downstream depends on it. A left-chest logo is usually 75 to 90 mm wide, a cap front about 50 mm tall, a jacket back 250 mm or more. Digitize at the size you will sew: scaling a finished design changes its density and its pull, so a design stretched from 60 to 100 mm sews thin and gappy.
Check the smallest element before you commit. If the logo has a tagline, that tagline sets the minimum size for the whole design, not the logo mark.
Drop the artwork on the canvas as a backdrop and lock it, then trace with the pen tool. Draw the shapes that sit behind first, because that is the order they should sew: background areas, then the shapes on top of them, then outlines and text last so nothing distorts them.
Density, underlay and stabiliser follow the garment, not the logo. A polo shirt and a fleece need different numbers for the same artwork.
On a scrap of the actual garment, with the actual stabiliser. This is the step people skip and then repeat twenty times. What it catches: registration gaps, letters filling in, puckering, and colours that looked fine on screen and vanish on a dark shirt.
You can auto-digitize one, and for a flat two or three colour logo the result is usable. A photograph or a gradient is not: embroidery has no tones, only thread, so somebody has to decide where the edges are. Auto-digitize is a starting point you then edit.
The limit is usually the smallest lettering in it. Satin text needs about 5 mm of cap height to read, so if your logo has a tagline, that tagline sets the minimum size for the whole thing.
Between 75 and 90 mm wide is the usual left-chest size. Digitize at the size you will sew: scaling a finished design up or down changes its density and its pull, so a design stretched from 60 mm to 100 mm will sew thin.