The VSCode team has developed a Live Server extension with a lot of integrations. See v1.58 pre-release notes:

Live Preview

We have developed a Live Preview extension, which hosts a local server for web development previewing!

It features an in-editor browser preview, live preview refreshing (on file change or on save), multi-root support, and more!

The extension also has a Live Preview task, which runs a persistent server and allows you to view server traffic and its associated files.

To learn more about what it can do, view it in the marketplace or check out its repo.

For Windows - Open your Default Browser - Tested on VS Code v 1.1.0

Answer to both opening a specific file (name is hard-coded) OR opening ANY other file.

Steps:

1. Use ctrl + shift + p (or F1) to open the Command Palette.

2. Type in Tasks: Configure Task or on older versions Configure Task Runner. Selecting it will open the tasks.json file. Delete the script displayed and replace it by the following:

   {
       "version": "0.1.0",
       "command": "explorer",    
       "windows": {
           "command": "explorer.exe"
       },
       "args": ["test.html"]
   }
   

   Remember to change the "args" section of the tasks.json file to the name of your file. This will always open that specific file when you hit F5.

   You may also set the this to open whichever file you have open at the time by using ["${file}"] as the value for "args". Note that the $ goes outside the {...}, so ["{$file}"] is incorrect.

3. Save the file.

4. Switch back to your html file (in this example it's "text.html"), and press ctrl + shift + b to view your page in your Web Browser.