What gun does leon start out with in Resident Evil 4

It's an original design; it doesn't exist in real life. According to the canon of RE4, it's a customized handgun made by (Joseph) Kendo -- the same man who made the Raccoon City S.T.A.R.S. Samurai Edge. It is chambered for 9mm Parabellum, and has an initial capacity of 10 rounds. The weapon lacks a real name, and is usually referred to as The Handgun.