A deck I used through the core box and Shadows of Mirkwood with a Hobbit companion deck: The Road goes ever on and on. The two decks won all scenarios (including Dol Guldur) with over a 50% win rate.
Since the hobbits have low starting threat and good threat reduction themselves, I want to use Galadriel’s ability to reduce threat and draw card to build up. This deck starts as first player to use Bilbo’s ability immediately. First priority is Unexpected Courage and Nenya on Galadriel. Defense buffs go on Amarthuil, who will want to engage for resources and to make Halbarad a free quester. Songs and signals can be played on hobbits if they have renewed friendship for extra card draw or threat reduction. If you get Love of Tales out in either deck they become free or a net +1 resource. Song of Earendil can be put on either hand in response to threat needs.
The deck searches and draws a lot of cards, often going through the whole deck. Once Silver Harp, Mirror and Unexpected Courage is on Galadriel, you can cherry pick a card every turn in excess to the 2-3 cards.
I played through the first nine scenarios with a bonus hand of ten cards from which to swap cards for certain scenarios (mainly Journey to Rhosgobel), but also to try out some new (to me) cards. The following 10 cards were sometimes used instead of other cards:
Feint
Dunedain Mark
Fornost Bowman
2 x Power of Orthanc
A Burning Brand
2 x Athelas
The Long Defeat
Steed of Imladris