How do I get the class attribute value using jquery and javascript

You should change:

onchange="startFilter();" to onchange="startFilter(this);"

and in startFilter function:

function startFilter(ele){
    var className = $("option:selected", ele).attr("class");
    if(className == 'type'){
        //do something
    }
}

Take note that, the this inside startFilter function refers to the window object, not the element you bind it to.