Welcome to the game! I remember the first time I played Passage Through Mirkwood with one of the core set decks--it was terrible! It was a long time before I was able to move on to Journey Down the Anduin, and I've still only beat Escape From Dol Guldur a few times. (Never solo-playing!) Here are some specific strategies and reminders that are absolutely essential for tackling the game as a beginner with a limited card pool:
-Keep your threat low for the first few rounds of Journey Down the Anduin, long enough to draw a Forest Snare. That's one of the only viable ways of dealing with the Hill Troll, working with the Core Set cards.
-NEVER play Tactics mono-sphere. There's only a total of 4 Willpower in all of the Tactics heroes and allies in the Core Set. The temptation to go all-out monster-killing is tough to resist, but without multiple decks, mono-sphere Tactics is a notorious nightmare.
-Probably for Journey Down the Anduin and DEFINITELY with Escape From Dol Guldur, play with either another player, or, if that isn't an option, play with multiple decks.The core set in itself doesn't come with near enough cards to use any full strategy playing with the preset decks, so it's always best to combine some of the spheres.
-If you get beat over and over again on any of the quests, don't give up. I remember wanting to sell the game when I first got it. I'm so glad now that I didn't.
I hope you have some luck and enjoy questing! LotR LCG has been one of my favorite FFG games.