i screw all day
boilers radiators showers pipework baths loos floorbaords etc etc etc i only have 1 drill 6.5mm masonary, i use brown plugs and either 1 or 2 inch size 10 or 12 screws thats all you need full stop.
if the wall is plasterboard use the screw in fittings with internal screws no drilling req.
the secret is keep consumables to a minimum and you always have everthing you need 1 drill bit 1 size plug 4 sizes of screw 1 size two 12 inch screw driver.. simples
you only have to drill the hole as deep as the screw push the plug in ( use the same shape as the photo above) and screw away