Agreed. Beat every class in solo play and try to get every class to level 10 just to unlock all the basic cards and make it possible to do quests.
Level for each class has nothing to do with matchmaking. It allows you to unlock premium cosmetic rewards for class spells, and at high levels for the neutral basic cars and even your hero card. It's all just bling though, getting to level 10 is the last unlock.
Use the quest gold to build your collection. The Naxx pack has several wings with good rewards so it's worth trying to unlock it for cash ($25 for all 5 wings) or gold if you can save up that much. reddit has several guides you can find to help beat the bosses and earn those cards.
Specific to Warlocks, the Zoo style deck is quite cheap to build and can pull out wins against any other deck. It's the same concept as the MtG Zoo deck, lots of dudes, trade more efficiently, use the hero power to build card advantage, batter face when the board's clear and swing for the win. The new expansion added a few new creatures to choose from, but the core concept is still the same as since launch. Handlock is a much larger investment in rare/epic/legendary cards but plays a lot more like the MtG control decks.
Playing Arena is like MtG sealed deck/draft hybrid where you don't keep the cards when done, play until you lose 3 matches or win 12. Costs 150 gold (aka 1.5 packs) but the reward is at least a pack and if you go 3-3 you'll probably end up breaking even or just slightly ahead. Go 7-3 and you'll have a good chance of getting about 150 gold back and go infinite while building up free packs. If you don't have a plan to buy random packs for cards, arena can be a good investment and let's you play a few other classes.
When you get a quest for 60 gold and you have to play priest or paladin for it, you'll be thankful for having the basics unlocked and having played it once or twice in arena. Also, if you have a wowhead account from playing WoW, you can use http://www.hearthhead.com/collection to put your cards in and sort their deck database for decks you can build.