This is not a very precise question. But to help you to get started, I can say that:
tomcat and jetty are both Java Application Server. They don't provide specific support for REST/SOAP technologies. They are just Servlet Container. But : your webservices will be implemented by one or more servlets. So a ServletContainer is certainly something that will be part of your stack. (Tomcat is widely used).
once you have an ServletContainer you can choose some framework to help you. Spring framework is a lightweight framework helping you to bring everything together. Configuring all your components etc... It provide built-in support for REST/SOAP, but it can also be integrated with more powerful-webservice-dedicated frameworks.
for REST implementation, I recommend Jersey (the reference implementation). It can be integrated with Spring quite easily.
for SOAP : you can look at apache CXF (it also provide support for REST)
So, you can look at : Tomcat + Spring + Jersey + CXF. In my opinion it's a good opensource stack to start with webservices.