The +P you see on cartridge boxes denotes that the round is loaded to approximately 10% higher chamber pressure than the standard round. These standards are set by the Sporting Arms Ammunition Manufacturer's Institute, or SAAMI. They only list +P for 9MM Luger (9X19, 9MM Parabellum, or most commonly just called 9MM), 38 Special, 38 Super ( a somewhat obscure round for semi-auto handguns), and 45ACP.
Several manufactirers sell what they call +P in other calibers, but there is no standard as to how much they are loaded over maximum standard pressure, if at all. Other than in the 4 listed rounds, if it says +P it's advertising hype at best, dangerously overloaded ammunition at worst.
In your price range either a S&W 686, at the top of your economic limit, or the Ruger GP100 at a lower price point would make an excellent choice. With the gun chambered in 357 Magnum you get plenty of performance when you want it, but have the option of using more economical, and lighter recoiling 38 Special ammunition for practice, and plinking.