Things for newcomers to do before they even consider building a proper deck and taking the game seriously:
1) Unlock all 9 heroes by defeating the AI – Allows you to use alternate heroes and completes “Ready to Go!” quest for 100g.
2) Get all 9 heroes to level 10 – Unlocks the Basic Set of cards for all heroes and completes the “Level Up” and “Got the Basics!” quests for 100g each.
3) Defeat all the Expert AI – It’s good for practice and it completes the “Crush Them All!” quest for 100g.
4) Complete a game in Play Mode – Completes the “First Blood” quest for a free pack of cards.
5) Disenchant any common card from the pack you got that you don’t want (Only Expert cards can be DE’d, Basic/Soulbound cards can’t) – DE’ing your first card gets you a bonus 95 dust. Use this dust to craft Ironbeak Owls or Spellbreakers (I’d suggest one of each but you can do two of one, if you prefer. Silence is invaluable in any deck).
6) Put together a deck with your new cards and play three games in Play Mode – Completes the “The Deulist” quest for 100g.
7) Once you’re comfortable with the mechanics, even if you aren’t very good yet,enter the Arena – Your first game is free and you are guaranteed a pack of cards and one other prize. Free cards are always great.
8) Win 100 games – Completes the “Chicken Dinner” quest for 300g.
Congrats, you’ve finished all the newcomer tasks and have earned yourself: 2 packs, 95 dust, 800g and whatever your second prize from Arena was! Use your rewards to buy more packs or more Arena runs (You risk very little by choosing to play Arena yet can gain a lot if you do well. I’d suggest always doing Arena). There is also the “Big Winner” quest that requires 1000 wins but that will take a few months for the casual player.