Once I've created your JavaScript, how do I get it assigned to a button that I can add to the toolbar without buying a toolset? Thanks!

If you have Adobe Acrobat DC Pro, you can also create custom commands to execute your JavaScript: Create Custom Commands in Adobe Acrobat DC Pro - KHKonsulting LLC

Read about the addToolButton and addMenuItem methods of the app object.

You can use the former like this, basically:

app.addToolButton({
    cName: "myToolButton", // internal name, must be unique
    cLabel: "My Function", // the text of the button the user sees
    cExec: "myFunction();", // the code to execute when the button is clicked
    cTooltext: "Click here to run my function", // the tooltip text for the button
    cEnable: true // when the button is enabled/disabled
});

And then your actual code is placed inside of myFunction:

function myFunction() {
    app.alert("Hello!",3);
}