I generally discourage actors from printing their own headshots because unless they have a lot of printing experience or want to spend a lot of time or money doing test prints and learning how to make it work, it's usually not worth it.
Most printers these days can print fairly clean images, but the tricky part is having to learn the right paper type and also having to learn how to get your name and inset border on the prints as well.
With a good printer (costing at least $500), ink can be as cheap as $.80 per page, with the paper itself costing about $.40 per page. This means it costs you about $1.20 per print. When you compare that with ordering 100 prints for $100, you can see why it's better to just get them made professionally. Large printing companies buy their ink and paper in bulk which means it's cheaper for them to print. Unfortunately for you, ink expires and you'd have to print many more prints than you'd need to be able to get value out of it.
If you don't want to invest in an expensive printer, ink and quality can cost a lot more. Sometimes it can go to $2.50 per page and the resolution will be low and colors won't match perfectly.
Most people opt to have them printed professionally because there's no learning curve and they don't have to invest a large amount of money in expensive printers and Photoshop software. And generally, the prints turn out better in the end.