java.lang.ClassNotFoundException: com.sun.jersey.spi.container.servlet.ServletContainer

You have downloaded Jersey 2 (which RI of JAX-RS 2). The tutorial you're referring to uses Jersey 1. Download Jersey 1.17.1 from (here), should be sufficient for you.

Jersey 1 uses com.sun.jersey, and Jersey 2 uses org.glassfish.jersey hence the exception.

Also note that also init-param starting with com.sun.jersey won't be recognized by Jersey 2.

Edit

Registering Resources and Providers in Jersey 2 contains additional info on how to register classes/instances in Jersey 2.

If you are using jersey 2.x then you need different configuration in web.xml as servlet class is change in it. you can update your web.xml with following configuration.

    <servlet>
    <servlet-name>myrest</servlet-name>
    <servlet-class>org.glassfish.jersey.servlet.ServletContainer</servlet-class>    
    <init-param>
      <param-name>jersey.config.server.provider.packages</param-name>
      <param-value>your.package.path</param-value>
    </init-param>
    <init-param>
     <param-name>unit:WidgetPU</param-name>
     <param-value>persistence/widget</param-value>
    </init-param>
    <load-on-startup>1</load-on-startup>
  </servlet>
  <servlet-mapping>
    <servlet-name>myrest</servlet-name>
    <url-pattern>/rest/*</url-pattern>
  </servlet-mapping>

Add this in pom

<dependency>
    <groupId>com.sun.jersey</groupId>
    <artifactId>jersey-server</artifactId>
    <version>1.17.1</version>
</dependency>
<dependency>
    <groupId>com.sun.jersey</groupId>
    <artifactId>jersey-core</artifactId>
    <version>1.17.1</version>
</dependency>
<dependency>
    <groupId>com.sun.jersey</groupId>
    <artifactId>jersey-servlet</artifactId>
    <version>1.17.1</version>
</dependency>