Play Tavern Brawl this week, it's a random brawl so this is the perfect opportunity to obtain a few more cards since your just starting and need a boost in your collection. Just practice it and you'll master it very quickly and try to win 30 games per day and just focus on rise of shadow or boomsday project packs. Try and mix then in over the week and you'll improve.
The Tavern Brawl really fun this week and even I'll be grinding it out until next monday.
Most of the time, it should be one week a build-ur-own deck and the other will be random deck brawl. Try aiming to play lots of random brawl when they come out. It will give you the chance to play cards that you don't own making the game fun for newer players and it gives you (sometimes) a more even-steven game.
However, I'd skip the build-ur-own deck brawl as you'll just get recked by the more experienced players out there, been playing for 5 years and I still get recked. However, do try to win your free brawl pack every week no matter what brawl it is. If you concede a lot of games because you just cannot win with the cards(tools) that are sufficient at the build-ur-own deck brawl, you will eventually find an opponent that will either auto-concede when you start (I find this usually happens after 5 or 6 loses in a row) or they will auto-disconnect meaning you have to wait threw the mulligan and they rope out turn 1 and 2, by 3 they should blow up. Just win 1 match at build-ur-deck brawl and call it a week for tavern brawl. Other than that, when it's random brawl, a good time to grind gold.