Peter,
I’m afraid static web projects cannot be deployed using Tomcat server, instead it can be deployed using HTTP server. You can configure such a server in MyEclipse 2015 from here : New > Other > Server > Basic > HTTP Server. You should see the field ‘Publishing Directory’ which can be set to your local folder (or Tomcat deployment location) in the HTTP Server wizard.
If you want to create a new static web project then you should enable the WTP Extras (Window > Preferences > General > Capabilities > Advanced > MyEclipse Standard Tools > WTP Extras). Once enabled, you can create the static web project from : New > Other > Web > Static Web Project.
I suggest you to download our latest version, MyEclipse 2015 from here, install it alongside your existing MyEclipse 2014 installation and give it a try.
Hope this helps and let us know if you see any issues with MyEclipse.