Ahh. So the question is concerning filters and tying the check boxes to fields.
This bit of code creates a checkbox which sets two fields, status and datecompleted, of the selected task tiddlers. I used an invisible button because I wanted to change two fields. If I only wanted to change one field, I could have used the same code you used.
<$button class="tc-btn-invisible" set="!!status" setTo="Done">
<$action-setfield datecompleted=<<now "MM/DD/YY">>/>
<input type="checkbox">
</$button>
Using a filter that looks something like this as part of your list:
<$list filter=[tag[task]has[modified]sort[title]field:status[Done]]>
<$link to={{!!title}}><$view field="title"/></$link>
</$list>
will give you a sorted list of the tiddlers which have the tag "task" and the field "status" with the value "Done".