The package.json scripts section should look like:

"scripts" : {
	"build": "tsc",
	"prestart": "npm run build",
	"start": "node out/index.js",
	...
}

My tsconfig.json is looking like this:

{
    "compilerOptions": {
        "outDir": "./out",
        "rootDir": "./src",
        "sourceMap": true,
        "moduleResolution": "node",
        "target": "es5",
        "experimentalDecorators": true,
        "emitDecoratorMetadata": true
    }
}

To run just use:

npm run start

For debuging in vscode here's launch.json:

{
    "version": "0.2.0",
    "configurations": [
      {
        "type": "node",
        "request": "launch",
        "name": "Launch Program",
        "program": "${workspaceFolder}/src/index.ts",
        "preLaunchTask": "tsc: build - tsconfig.json",
        "outFiles": ["${workspaceFolder}/out/**/*.js"]
      }
    ]
  }

Cheers!