Hello Cliff,
Thanks for trying out MyEclipse. In order to get a more complete picture of how working with WebProjects works in MyEclipse have a read of our WebProjects Development quickstart: http://www.myeclipseide.com/images/tutorials/quickstarts/webprojects/
And to answer your question more directly, you would want to use our “Exploded Deployment” when you deploy to your app server. This way ever time you make a change to a resource (.html,.jsp etc) that resource is automatically updated in your app server deployment without having to restart the server or web app.
Also, instead of using an external browser, you can launch our own internal Web Browser that is integrated into our workbench. Access this by clicking on the “globe” icon just to the right of the server manager icon in the main eclipse toolbar. Note that in upcoming versions of MyEclipse we are going to be making rapid improvement to this integrated browser as our Web 2.0 / AJAX tools continue to grow and mature.
Always remember that the support staff is here to make your MyEclipse development or transition as pain free as possible 🙂