My suggestion is that you first remove the 1.3 SDK and upgrade to the latest 1.4 version, then install either the latest Tomcat 4 or 5. Personally I think the Tomcat 4.1.30 is the most stable, but if you want to use the latest Servlet APIs, that means Tomcat 5.
Take a look at
http://jakarta.apache.org/tomcat/ to get started.
Classpath is only a problem when compiling, Tomcat totally ignores the classpath environment variable.
I seriously recommend that you use
Ant for compiling servlet projects in order to get control of classpath issues - there is a bit of a learning curve but it is worth it.
Bill