Firstly, Frodo offers the ring to Gandalf, for he is of it's power and does not think he can be trusted with it. Gandalf realizes that if he had the ring, he would've been corrupted by it, and as such refuses.
The ring is never offered to Legolas.
The ring is never offered to Sam, although he offers to carry it in some cases, and before Frodo was dragged to Cirith Ungol, Sam did take it off of him.
The ring is offered to Galadriel, but she declines for the same reasons as Gandalf.
Secondly, the main theme represented by Aragorn would be You cannot judge a book by its cover.
The other ones don't make too much sense.
Aragorn certainly did not believe in might makes right.
While Aragorn's love story was present in the book, it was far from his main theme, and Arwen rarely appeared.
And while the concept of All good things must come to an end is in the book, it is not represented by Aragorn. It is represented by the elves and their leaving from Middle Earth, Aragorn shows new birth with the kingdom of Men.
Hope this helps :)
