The easiest thing to do, is to download the ".exe" version of Tomcat.
Installing this way is the same as any other windows program. You double click on the exe and a wizard takes you through the process. One of the options will be to install as a Windows service. This will also give you start menu items, including a Tomcat configuration tool that can be used to change things like the JVM and heap size.
When installed this way, Tomcat will redirect all the logging that was going to your console to the log files under Tomcat/logs.