Insert new record in custom object using visualforce pages

I have a very simple Visualforce Page with using custom object called employee__c

I'm trying to save the data whatever the user have entered in the page, but I'm not getting any error from my below code but the page is blank not showing any input fields at all....

here is my VF page code:

<apex:page Controller="EmployeeController" >
  <!-- Page Header -->
  <apex:sectionHeader title="Employee Edit" subtitle="New Employee" />

  <!-- Begin Form -->
  <apex:form >
    <apex:pageBlock title="Employee Informations" mode="edit"> 

      <apex:pageBlockSection columns="2" showHeader="true" title="Information"> 
        <apex:inputField id="firstName" value="{!emp.First_Name__c}" required="true" />
        <apex:inputField id="lastName" value="{!emp.Last_Name__c}"  required="true" />     
      </apex:pageBlockSection>
  </apex:pageBlock>
  </apex:form>
</apex:page>

my controller:

public with sharing class EmployeeController {

    public ApexPages.StandardController controller; 


    Public Employee__c emp = new Employee__c();
    public Employee__c getemp()
    {
        return emp;
    }

    Public String First_Name {get; set;}
    Public String Last_Name {get; set;}  


    public EmployeeController(ApexPages.StandardController Controller)
    {
        emp = (Employee__c)Controller.getRecord(); 
        this.controller=Controller;  
    } 
    public PageReference save() {
      insert emp; 
      return null;
    }    
}