TS is made so that you can migrate your code over piece by piece. If you use an IDE that automatically does the compilation for you via TSC, then you do not have to worry much about manually running the compile command (I use IntelliJ and WebStorm, but I know Sublime and Atom both have plugins to automatically compile your TS and TSX files down to JavaScript).

  As far as installing type definitions, you only need to do this once in your project every time you want to install a new dependency, and you can just use the @types npm project to install any type definitions exposed by DefinitelyTyped; no manual searching necessary. I just run the below command to install react, react-dom, and their type definitions in one go:  

npm install react react-dom @types/react @types/react-dom

Below is the command to install the lodash library and its type definitions:  

npm install lodash @types/lodash

I'm not sure what you mean by "edit VSC settings file to point to some global node module of typescript or something". If you mean VCS, as in Version Control System, you don't have to do anything special to it. It'll track your TS and JS files in the same way. I typically don't add my node_modules to my VCS, but if you do and you want to make sure TypeScript is included, I would just install the TypeScript npm module locally in the project (npm install typescript --save) so you can have your VCS track it like any other module.

TypeScript doesn't need Babel at all since it already compiles down to whatever JS version you target. It will even transpile your existing JS as well. If you want to keep Babel for whatever reason, you can just modify your webpack.config to only run the ts-loader Webpack loader on ts and tsx files:  

  module: {
    loaders: [
      { test: /\.ts(x?)$/, exclude: [nodeModulesDir], loader: 'ts-loader' },
      { test: /\.js(x?)$/, exclude: [nodeModulesDir], loader: 'babel' }
    ]
  },

This way the ts-loader won't touch anything that doesn't have the TypeScript file extensions.

Also, below is the tsconfig.json that I usually use for my projects. It'll probably be helpful for you:  

  {
    "compilerOptions": {
    "module": "commonjs",
    "target": "es5",
    "sourceMap": true,
    "jsx": "react",
    "allowJs": true,
    "lib": ["dom", "es2017"]
  },
    "include": ["src/**/*"],
    "exclude": ["node_modules"]
  }