Several years ago a friend and I decided to watch the extended DVD versions of all three films in one day. We watched The Fellowship of the Ring, then had lunch. After lunch we watched The Two Towers followed by tea. After that we watched The Return of the King. It's a great way to appreciate the story, but not one I'd repeat in a hurry.
As someone who has read The Lord of the Rings many, many times the films follow the story in the books really closely, but there are a few stupid changes and additions that really, really annoy me. But, having said that they are excellent films and I'm sure you'll both enjoy watching them
In my opinion, you're not missing much. The Hobbit is over long. They spanned LotR over three movies, then spread The Hobbit, which isn't even half the length of Fellowship over another three movies*. They also made some additions that are not in the original in, in my view an unnecessary, attempt to fit in with the LotR movies**. I've watched The Hobbit movies once and have no desire to watch them again.
* Some cynical people, including me, thought this was a way to con more money out of LotR fans.
** In reality it was the other way round, parts of The Hobbit were rewritten to fit in with LotR.