What kind of competitive handgun shooting?
If for NRA Conventional Pistol (bullseye) you need a very accurate gun. A Les Baer or Rock River hardball or wadcutter gun lists for about $1700, maybe you could find one for $1500.
Or buy something ordinary (less expensive) and figure on having it accurized by someone like Alan Tanaka when you have learned the ropes and need more out of the gun.
If for an action sport like IPSC or IDPA, accuracy is less important and you can get into a gun for that anywhere from a $550 Taurus on up.