This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Renaming your webapp to ROOT and placing under the webapps directory is the easiest way to deploy it as the root app on the server.
Tomcat, pretty much ships in production mode. I usually change thing more for development mode.
You might want to un-deploy any of the apps that ship with Tomcat (unless you're actually using them).
I keep the manager app around but I re-name it. I also turn off directory browsing (from conf/web.xml) and build my own 404 error page that doesn't show the make and model of the appserver to any would be cracker.