In the ProMaker line of button making equipment there are two types of 3 inch and 3-1/2 inch button makers, standard and photo. The standard machines are what you'll need if you intend to print your button graphics on an inkjet printer or a laser printer. You pretty much only need a photo version if your paper is super thick. You don't need to use super thick paper in a home printer to get good quality you just need to use the right paper. 

The only time you would need to use super thick paper is if you're doing on-site buttons and using a high speed event printer, or prints from a photo lab, or some special project with uber thick paper.