[Imladris]

I believe I heard years ago, that the Ring symbolised pure evil. Thus, inevitably, Frodo would be affected more than Sam. As for Bilbo, the Ring was asleep...it's power of evil was not awake, and thus could not do as powerful and lasting damage.

As for Frodo's hopelessness, I'm also not convinced of that.

Still round the corner there may wait
A new road or a secret gate;
And though I oft have passed them by,
A day will come at last when I
Shall take the hidden paths that run
West of the Moon, East of the Sun.

This was the song that Frodo sang as he left the Shire. It doesn't quite have the ring of despair to me.