Jake
Maybe you could post some pictures of your new yard to get a feel for what might be appropriate?
Any climbing plant could use the chain link fence and hide it at the same time. Easy morning glories, sweet peas, thunbergia for example. But they would only be as high as the fence and not necessarily enough for privacy, just something to hide the fence.
And are you asking for suggestions just for a wedding to make the place look nice and not necessarily a vegetable garden?