dropdown lists do not use a "value" attribute, they use <option> elements with value attributes and a selected state. To default a selection in a dropdown you simply have to add a 'selected' attribute to the option element you want selected.
<select name="my_dropdown_list" id="my_dropdown_list">
<option value="0">-- No Value --</option>
<option value="1">First</option>
<option value="2">Second</option>
<option value="3" selected="selected">Third</option>
<option value="4">Fourth</option>
</select>
As far as checkboxes go, you use the "checked" attribute to default its checked state, like this:
<input type="checkbox" name="my_checkbox" checked="checked" />
Now when coupling this with your server side code, you just need to use the right conditional logic to get your markup to look like this. I would highly recommend NOT using your superglobal vars directly in your views like that. But I am sure you're only doing that for testing and development at the moment.