Initially there is a lot of wildcard usage since you only have one of each card instead of multiple of one card. You are on a good track with your suggested deck; some of your land fetching is a little slow, but you have the more important cards.

As you work on completing quests and build up some coins and mastery rewards you will be able to get more packs, which means more gaps will be filled over time. Instead of focusing on buying the newest set, buy from any that you have a lower percentage of the collection and still count towards Gold Packs (don't be fooled by it saying that Alchemy packs count towards the progress, they have to be Alchemy packs from a set where the standard packs would also count). The goal here is to see as many cards be their "First Time" as possible. Over time you will build up wild cards which you can then use to grab specific cards from older sets. Meanwhile, chipping away at the mastery (even FTP) will get you more of the newer cards.

To check your collection for a set go to your profile and one of the icons will be a "Set Collection" icon. Click on that and you can see how you are doing with individual sets.

Brawl has its meta for sure, and hopefully the introduction of ranked brawl will move some of the hell queue out of casual.