Many people start their embroidery business with a home embroidery machine. They vary in costs depending upon the size of hoop they can handle and the features they offer. Home machines can cost between $150 to around $7,000.
Brother offers a 6 needle machine that is mid way between home and commercial. Happy makes a machine that is a good starter commercial machine, but so do many companies.
The cost of stabilizers, hoops, thread, needles and software is often not included in the price. Software is needed to do any designs.
If you are looking for a commercial machine, check Beacon Funding. They offer used machines and handle funding for them.
As for patches, if you plan to do your own morrowing you may want to look into a specialty machine for that. (Morrowing is the satin edging on patches)
Or you can purchase pre-made blanks with the edging finished.
Sorry, I do not have inforamtion on how popular patches are.