Based on my experience, Flametongue Totem is your friend. Most of your minions provide value just by being played unlike lets say, The Lich King, Vicious Fledgling and other cards you want to keep on board for a bit longer.
Priority is to have your starting hand on curve instead of fishing for specific hand. Fire Fly smoothes out the early curve perfectly with its battlecry.
Even if you mulligan terribly and are forced to hero power only during the early turns, eventually free Thing from Below + card combo will put you back into the game.
Things i always remove from starting hand:
Mana Tide Totem - During early game your hero power is good enough filler. Extra cards for transforming are good once you have mana to instantly evolve them.
Bonemare - Expensive.
Doppelgangster - While this is your main target to evolve, i prefer to have cards that can secure your early to mid game. If you have no board on turn 5 while enemy hero builds his freely, he will just SMORC you not giving much Fs about it.
Combinine this card with strong battlecry cards like Bonemare for extra value. Do not instantly end turn after you play it. Animation is long, and you do not want to miss possible evolves into charge minions.
Counters high synergy cards. Pirates, Murlocs, Taunt Druid, or you can deny some value away from Bloodreaver Gul'dan or similar, as the demons get transformed, not killed.
Your earlygame powerhouse. At 6+ mana turns you mostly want to trade/face and heal your minions by evolving them. Everyone is aware of this so do not be surprised if people blow their removals instantly on this card.
This card provides very good tempo. An extra token on board for your Flametongue Totem. Scarry if combined with Fire Fly at turn one.
Do not be scared to use this early to maintain tempo advantage. Without spellpower totem this is not consistent spell past earlygame.
Mana Tide Totem
Nothing to add here. If this card survives a turn it is safe to assume that the enemy doesnt have proper removal unless he plays much higher threat on the board himself.
Kills the midgame minions while also ramps up your evolve potential. Good way to get past the enemy Tar Creeper or Stonehill Defender
This card can be obviously used as a finisher. In evolve shaman you can use it as a board reset to trade your early little guys and totems into enemy minions before you bring your evolved Doppelgangster etc.
Thing from Below
Evolve shaman have pretty consistent curve compared to other decks and classes. However, when RNG avoids you like Blizz employees avoid EU forums, this can bring you back into the game.
Solid body, awesome battlecry. You will have plenty of minions for your Flametongue Totem to buff and you do not have to be worried about having unused mana at the end of your turns early on.
Fish for specific counters against enemy deck. Next to Flametongue Totem this improved version of Tar Creeper with offense included.
The battlecry power depends on the amount of Jade minions you played. The stronger the golem is, the stronger evolve it will become. However, when played with basic 1/1 it doesnt have that much presence on board so consider this fact when you might want to play some other card instead.
Saronite Chain Gang
More evolve friendly card than Stonehill Defender and not as easy to remove early.
Main target of Evolve. Pretty weak on its own. If RNG smiles on you, evolving theese is instant concede for the enemy :)
Think of the battlecry of either +4/4 charge, or something that can save one of your minions from trading to death for one extra Evolve target.
Ooooh i was so waiting for this. The only way this card has any sort of power, is next to Flametongue Totem, which is not always available on top of that. For the same mana, better play something that is useful on its own, and buff that minion instead.
While much better board clear than Maelstrom Portal i really dislike the overload part which harms you next turn.
Besides the fact that its not a budget card, this card helps in long games against control decks where you do well.
Master of Evolution
Transforming a single minion is not worth sacrificing Jade Ramp cards which add more consistency to the deck.
Except Doppelgangster followed by one or two Evolve, every card you have is playable on its own. Sometimes, if you can afford it, the only way to increase their value is by holding them in your hand for later turns.