Hi!
GlassFish is very nice, with a
servlet container, an
EJB container, a web service stack (Jersey), an excellent management console, a
SOAP web service tester etc already integrated and ready to use. This is definitely the option I would recommend for a beginner, since it will allow you to focus your effort on learning web services with a minimum of hassle.
Apache CXF, formerly XFire, is another nice web service stack which can be run in a
Tomcat instance and supports both SOAP and REST web services.
Axis2 is, as far as I understand, widely used. Don't know if it is THE most popular web service stack or not.
In my opinion, the important thing is to make sure that the web service stack you choose supports standards such as JAX-WS, JAX-RS (optional) etc etc. This will make it easier for you to find literature, examples etc. and also make your web services more interoperable.
Best wishes!