Setting Controller Variable from JavaScript and use the Variable for a Query

I'm trying to pass a JavaScript Variable to my Controller and do a query with the value.

Here's what I got (only necessary code):

My Controller:

public with sharing class MyClass{ 

public String AccountList { get; set; }        
public String myString {get; set;}

// Method for testing a hidden field functionality 
public PageReference myMethod(){
    System.debug('myString: ' + myString);
    return null;
}  

 ...
 public static String getlstAccount() {
    List < Accountwrap > lstwrap = new List < Accountwrap > ();


   String Abfrage='SELECT Id, Name, Phone, BillingCity FROM Account WHERE Id=\''+MyString+'\'';
   List < account > lstacc =  database.query(Abfrage);
   ...}

My VF Page:

<script>
function setVar(param){
jQuery('[id$=myHiddenField]').val(param);
passStringToController();

var List = {!lstacc};
}
</script>     

<apex:form >
    <!-- Hidden field to store a new value of the variable -->
    <apex:inputHidden value="{!myString}" id="myHiddenField"/>

    <!-- Action function for the rerendering -->
    <apex:actionFunction name="passStringToController" action="{!myMethod}" rerender="myHiddenField"/>

    <!-- A command button for sending a call to the function -->
    <apex:commandButton value="Test me" onclick="setVar('new value'); return false;" />
</apex:form>

So I want to set the variable and change the AccountList (dependent on my variable) after the page is loaded.

I got the code for setting the variable in controller from another question, but it seems it doesn't work, and it's always null or empty. I think I'm missing something important.

Thanks in advance!