As I can get the value of a DropDownList in the controller, it is assumed that there is a DropDownList which when selecting an option and pressing search should filter and throw the data in the table below in that same view, I am working on the following way Is it the right way or am I wrong?
View: 
Driver: 
You are correct, from the DropDownList you can get the value and after that you can do the filter by pressing a button, or you can add the attribute AutoPostBack="true" to the DropDownList control and add the event OnSelectedIndexChanged . You have two ways to do it, both return the selected value.
DropDownList.SelectedValue;
DropDownList.SelectedItem.Value;
Here I leave the help of MSDN, here comes everything you need to know about the control DropDownList