So unfortunately I can't get out ot the store today to pick up some expansions as I had planned. Up until now I have been playing with the prebuilt 1 sphere decks just trying to get a feel for how the game works but with little success. I'm going to start building a multisphere deck but I was wondering if anyone had any suggestions for cards that I would put into this deck that would help me tackle all of the included quests in the core set. I'm experimenting as I write this and if I come up with anything good I'll post my results.

I don't know of any decks that will beat all three scenarios. With the core set you pretty much need to tailor your deck for each quest. But I must say that I'm surprised that you were going to buy some Adventure Packs without first trying to build a multisphere deck. They really aren't as scary as you might think. I remember being afraid of them my first time, but it wasn't that different from using two energy types in Pokémon. I would totally give it a shot, if I were you. Start with a dual sphere deck to take on Passage Through Mirkwood. I'm trying to remember what decks I tried . . . I think I did alright with a Spirit/Lore using Éowyn, Dúnhere, and Denethor.

yes this isnt really a game where you can make an all powerful winning deck- you need to do as budgernaut said and tailor it per quest

though a good starting point is spirit/tactics with-

eowyn- use to quest and buff up her willpower with her action

dunhere-use to attack enemies in the staging area, or just in general attacks

thalin- defend/attack and commit to quests to deal 1 damage to enemies as they are revealed

include these cards ALWAYS if you can fit them in

UNEXPECTED COURAGE (spirit)

TEST OF WILL (spirit)

HASTY STROKE (spirit)

NORTHERN TRACKER (spirit)

these are the most useful cards amongst a few others

some of the most powerful cards in the game are in core... apart form the ones rich mentioned, tomb, stand and fight, greeting, gandalf.. man.. so many good cards I can not be bothered listing them

If you look the decks people are posting at cardgameDB you can see that the majority of decks are still mostly core.

That being said while it is fairly trivial to beat Audin and Mirkwood in core with a single copy of core.. escape is extremely hard. In fact it wasn't until the release of Ziggy y in Khaz that escape has been moved into my mental "conquered" pile. As now it is easy to solo this quest and be garenteed to win in most attempts.

This is going to happen all though out the game life, as you get better cards pools quest will get easier and new quest will be harder. Unlike a traditional game like coc for example, you can not really pick and choose what packs to get, no matter what FFg tell you.

if you buy a dorrowdelf pack it will be so hard if all you have is that pack and khaz... to play this game you really need to buy some key packs form every cycle.

As for a deck, I know Tragic and he is planning to do a lackeyccg video of all the core quests done with a single copy of core... so a cool demo for you should be up for you soon.