So, i'm new to C# and not really sure how to do this. I need to create an options table where when the user loads it, it looks sort of like this http://img11.imageshack.us/img11/9012/formf.jpg

On the initial load, all of the data members are on top, loaded from an array. If the user doesn't want a particular data member to be used all they have to do is highlight it and click the down arrow. This moves the entire row from the top table to the bottom table visual wise, and to a different array data wise. I assume I would use something like a ListView, but I'm not sure how to make it behave like I want it to. When the user clicks a row I want the whole row to be highlighted, and I would like the give the user the ability to sort all rows by a particular column.

Its all basic list view control stuff. the list view can be difficult to work with, I recommend a ListView control tutorial. there are many. If I were to explain to you all that your question entails inside of this reply, it wold practically be a book.

here's a good start:
http://programmerslog.wordpress.com/2008/07/18/using-listview-control/

But that's just a start, google around, there are some good articles out there.

The jpg I looked at seems like it would be more suited for a DataGridView with a DataTable as its DataSource. Why have you chosen to use a ListView?