+1 to using cabinet screws. Do not use drywall screws, your cabinets can actually fall off the wall with this type of screw ( it pulls through the hang rail and remains attached to the wall while your cabinet is on the floor).
Also make sure you account for the height of your flooring. You don't need to install your flooring under the cabinets, but shim the bases up that dimension from your finished floor height, your dishwasher will need to fit into the cavity below the countertop with the flooring installed underneath, you don't want to block it in. Your upper cabinets should be hung 54" from your finished floor height.