No,
you should be ok to start off with just tomcat, without having to install apache http server as well. tomcat comes with its own http server built in, it will run on tcp port 8080 after it is started.
for windows installation, see the documentation here
http://tomcat.apache.org/tomcat-6.0-doc/index.html
you want the .exe installer, it will use a wizard like installer that will create a windows service and have tomcat started for you on windows startup. there should be a start menu shortcut for tools to start, stop, inspect tomcat server status.
basically, once you have at least a Java runtime installed (but should likely have the JDK to compile java sources anyway, since next steps would be to create web applications right.
other tools that might come in handy is "Ant", which uses an xml file to define tasks such as running the javac compiler on sources and then the jar command to package the application into a .war file. which can be deployed into your tomcat instance. but for starting out you could likely create a folder inside the webapps folder of tomcat, starting with an empty WEB-INF/web.xml is all thats needed for tomcat to recognize the folder as a web application. though this is usually inconvenient. its handy to learn how to use
ant scripts to package war files and the tomcat deployer to publish them.
If you don't use an
IDE yet, eclipse has a good
j2ee developer edition of their ide, that lets you create a dynamic web application project and launch it, or even step through it in a debug mode, inside the IDE. they do this by connecting or attaching to a tomcat instance that is installed already on your system, or installed just for use with eclipse. its a bit of time to set this up the very first time, but the here is a good manual on this :
http://www.windofkeltia.com/j2ee/wtp-tutorial.html
then later on when comfortable using tomcat on its own, it could be connected to apache using mod_jk (in the tomcat connectors project)/