This is a dangerous time to be writing this particular article; I'm writing this shortly before the release of Tarkir: Dragonstorm. The set comes out tomorrow, which means any predictions I make could be proven laughably incorrect by the time the article is released. So, what I'm going to do, rather than trying to predict the best non-rares in each colour or each clan, I'm going to discuss a few of the cards that looked good during the early access event last week.
Osseous Exhale
This is a bit of low-hanging fruit, perhaps, but Behold a Dragon looked easy enough to activate in a lot of the decks I've seen streamers playing. Obviously this card would be playable in control decks and borderline-playable in aggressive decks without the kicker, but the extra two life is very relevant for decks that want to stay alive to the late game.
Sibsig Appraiser
I've heard numerous streamers refer to this card as Organ Hoarder, and it's easy to see why. A three-mana 2/1 that draws a good would already be pretty good, but binning a card can very easily be up-side in this format. This card has looked excellent every time I've seen it cast, and I can't wait to try it for myself.
Feral Deathgorger
This is a common?! It does everything: draws a card, pumps your creature (helping with the counter synergies abundant in Abzan) and hoses opponents that are relying on their graveyard. This card just does so many things, and all of them are good for you.
Venerated Stormsinger
While this card doesn't do everything, the one thing it does do is take over a game if left unchecked. At face value, it's a Hill Giant that drains for one every turn. That's the floor, but the ceiling is pretty much "winning the game." The drains add up real fast, and if you have any kind of reasonably even board state, you'll be singing your opponent a goodnight lullaby in no time.
Equilibrium Adept
While I mentioned in my last article that I was unconvinced by Flurry, this is the card that came closest to changing my mind. A 2/4 double strike creature is no joke, and the fact that it sometimes spots you a trigger next turn really helps to ensure that the Adept is turned on more easily.
Traveling Botanist
If you're interested in filling your graveyard, this card is great. If you're interested in making sure you hit land drops, this card is great. If you're interested in attacking on turn three, this card is... pretty good. Like a lot of cards on this list, the Botanist is versatile. It's not amazing at anything, but it's good to great at several things - and they're all things you want to be doing in limited.
Cori Mountain Stalwart
I love how this card does two diametrically opposed things in two different styles of deck. In an aggressive Mardu or Boros deck, this is some nice reach and some leverage in a race. In a Jeskai "Cheons" deck, the Stalwart is great at keeping you alive long enough to cast some absurd rare like Jeskai Revelation.
Disruptive Stormbrood
Now this is some value. Kill a thing, make a 3/3 flier and kill another thing. This is a great nuts and bolts three-for-one, and the fact that you can split the cost up and only pay for the parts you need is a very juicy bonus.
Hardened Tactician
Okay, I haven't actually seen anyone play this card yet, but come on. This is definitely in the "would've been a rare in OG Tarkir" category, and since both of the Black-White clans are likely to have disposable tokens lying around, I expect this card to take over a lot of games. Try to play this on four mana if you can, so you get at least some value if (when) it gets hit by removal.
The Uncommon Clan Dragons
Each clan has a three-colour uncommon Dragon, and all of them are very good if you can cast them. I suspect that means that the Green ones should get a bump over the others, because you'll have access to more fixing, but they are all worth playing - again, if you can cast them. I think they are pay-offs for being in the right clan for your seat rather than being a reason to go into that clan in the first place, mind you. I don't think we're supposed to be first-picking three-colour cards, even in a set like this.