When you buy a new door knob, hinge, switch, wall outlet, or other hardware item that includes screws, always save the old ones. (The only exception might be if the screw heads are slotted and filled with paint and the screw is a common one.
Why? Have you priced screws recently? And have you tried to find exactly the screw you need that fits some arcane or 50-year-old item? I even take the wiring screws out of old outlets, since you never know when you might need one, and such an unusual, stubby screw would probably cost a dollar or two at the hardware store. I've found that those "screw assortments" have none of the commonly used screws in appliance or electrical repair.
I just installed an outdoor cover for a GFCI and the accompanying screws did not fit--too long. I had to scavenge the screws from a wall plate cover because I didn't have any spares.
You'll end up, of course, with a jar filled with an amalgam of miscellaneous screws, but think of the pleasure of fishing through it sometime in the future and finding just what you need.
