If you are not seeing a product when you go to sell it, its POS Visibility is probably not checked. To fix this, go to Products>Products List (General tab), view the desired product, check the POS Visibility box as shown in the attached image, and click Save. 


Similarly, the Site Visibility checkboxes affect at which location the buttons are shown. 


To make the "quick button" for a popular product visible on the POS, go to Products>Product List, view the desired product, and click on the POS tab. Check the "POS Quick Button" checkbox  as shown in the attached image, and click Save.