Diameters are indicated by a gauge number. Many length and gauge combinations are available. Get stainless steel or aluminum screws for a project that will be exposed to moisture and brass or bronze ones to match hardware. Otherwise, you'll save using plain, plated, or galvanized screws. You can do most projects with either common or finishing nails.
Common nails have large, flat heads and are fine for rough work.
When appearance counts, select the thinner finishing nails. You can drive a finishing nail's head below the woods surface with a nail set and fill the hole with wood putty. Nails are sized according to the penny system, designated by a number and a d. Keep a block of paraffin in your workshop. Rub screws across it and they will penetrate wood with less difficulty.