Shortcut to push code to git in VSCode?

There is a button at the bottom left of the VS Code editor, which you can click to automatically sync your branch with that from remote (i.e. both pull AND push, merging your branch with upstream if necessary). This might or might not be what you want, but it's easy to click this when you know that there are no changes upstream (e.g. when you're working on a project by yourself).

Otherwise, I frequently bring up the Command Palette with ⇧⌘P (Ctrl-Shift-P on Windows/Linux) and type gpus, which brings up Git: Push as the first option. (It's been ingrained in my fingers since the days of Sublime Text)

If you are using the later versions of VS Code which has MRU list of command history, you can shorten it even further and just type gp, which is exactly what I've been using since SublimeGit in Sublime Text.

Lastly, another option you may want is to add a custom keyboard shortcut to push changes. You can do this by editing your Keyboard Shortcuts File, and adding something like the following:

{
    {
        "key": "ctrl+alt+p",
        "command": "git.push"
    }
}

There is a new setting Post Commit Command in vscode 1.30.1 to change the default commit behavior