Focus Input Box On Load

There are two parts to your question.

1) How to focus an input on page load?

You can just add the autofocus attribute to the input.

<input id="myinputbox" type="text" autofocus>

However, this might not be supported in all browsers, so we can use javascript.

window.onload = function() {
  var input = document.getElementById("myinputbox").focus();
}

2) How to place cursor at the end of the input text?

Here’s a non-jQuery solution with some borrowed code from another SO answer.

function placeCursorAtEnd() {
  if (this.setSelectionRange) {
    // Double the length because Opera is inconsistent about 
    // whether a carriage return is one character or two.
    var len = this.value.length * 2;
    this.setSelectionRange(len, len);
  } else {
    // This might work for browsers without setSelectionRange support.
    this.value = this.value;
  }

  if (this.nodeName === "TEXTAREA") {
    // This will scroll a textarea to the bottom if needed
    this.scrollTop = 999999;
  }
};

window.onload = function() {
  var input = document.getElementById("myinputbox");

  if (obj.addEventListener) {
    obj.addEventListener("focus", placeCursorAtEnd, false);
  } else if (obj.attachEvent) {
    obj.attachEvent('onfocus', placeCursorAtEnd);
  }

  input.focus();
}

Here’s an example of how I would accomplish this with jQuery.

<input type="text" autofocus>

<script>
$(function() {
  $("[autofocus]").on("focus", function() {
    if (this.setSelectionRange) {
      var len = this.value.length * 2;
      this.setSelectionRange(len, len);
    } else {
      this.value = this.value;
    }
    this.scrollTop = 999999;
  }).focus();
});
</script>