I'm decent at these sorts of games. I played Magic a LOT, and TRPGs are one of my favorite types of games, so I feel right at home with most of the mechanics. But since I won a lot, I quickly found myself in the Silver ranking. And now I'm doing 50% wins at best, because my "enhanced" starter decks just don't have the cards to compete. And it's not the Legendaries or Epics, either. It's just the non-default commons: the extra creature removals, efficient enhancements, more versatile dispels. I just opened another pack before coming back to this thread, and it was an excellent pack! An Epic, a Legendary, and 3 commons. The three commons went instantly into my decks, while the Epic and Legendary are sitting around in reserve.
For someone with a basic amount of cards, but still wanting to compete in Silver and probably make it to Gold, I would recommend Kara Winterblade of Vanar. The thing is, with her ability to buff every minion in your action bar for 1 mana, she can create an insurmountable amount of value that your opponents will find nearly impossible to deal with, even if they technically have better cards. In addition, Vanar has some of the best class removal spells in Chromatic Cold and Aspect of the Fox; both of which you get for free.
Here's a sample example deck I built at a glance:
Here's
a link to it with a lot more detailed information.
The only non-basic card in there is Dancing Blades, of which there are 3. It's a common card, and it's one of the best cards in the game, it fits into almost any deck, so I would recommend crafting it if you don't have them already. It's cheap and spirit well spent. It also creates one of the best combos in the game. Aspect of the Fox turns any enemy minion into a 3/3 wolf with no abilities. If you use that plus a Dancing Blades, you will kill any enemy instantly, no matter how powerful they are, while putting a 4/6 body on the board. It's one of the most devastating power swings in the game.
With Chromatic Cold and Ephemeral Shroud x3 you'll have 6 dispels, which is more than enough to deal with most provokes, deathwatch, dying wish, etc.
The key to using the deck correctly is to try and use your ultimate ability every time it's off cooldown. That way, the value of your minions just keeps increasing and increasing exponentially, and when you finally play them, the opponent will be unable to deal with the raw stats being thrown at them.
Try buffing your Saberspine Tiger as many times as you can before using him. A 4/3 or 5/4 with Rush for 3 mana is freaking scary. Use it to destroy problem minions or finish off the enemy commander.
Of course these are all basic cards, with the exception of Dancing Blades, so you can make some replacements since I'm sure you'll have quite a few cards that aren't. However, many basic cards are some of the best cards in the game, so it's not really necessary either. A deck like that should work fine.
edit: Made some deck changes to better reflect the current meta, links and explanation updated.