Supplying high quality Vector artwork, is the best way to ensure your designs will be duplicated as accurately as possible.
Vector graphics are easily scale-able without losing definition.
The most common graphics software for creating vectors is Adobe Illustrator.
If you have access to a Graphic Designer, they should be competent in this programme and you can ask them to create the right types of files.
Files will need all strokes created as outlines, along with text.
This should eliminate you having to send any font files with your designs.
Vectors will work well for both Embroidery & Print
For embroidery, vectors are not as essential, because an embroidery file will have been transformed into a ‘Stitch File’
This process is called digitising and the digitising software can use high resolution jpeg files.
A Word of Warning!
Avoid taking your artwork directly from your own website or the Internet.
These file will be low resolution and will create poor quality results for both print & embroidery.