The BGG strategy forums have much more information, see this really good thread A Collection of Opening Moves and First Round Strategies by Matteo Angioletti, explaining the 5 best openings for Baratheon (the link contains the openings of all houses)
Overall: Baratheon's main plan is to secure the castles on the eastern shore, using support from the sea. Your position will lead you to clash with Martell for Storms End, Tyrell for the Reach, Lannister for Harrenal and also Stark for Crackclaw Point and the Narrow Sea. Your main concern in the early game is to balance the spread of your forces as you don't have any supply immediately available (Blackwater should be one of the big objectives in the first rounds for you to achieve, as it grants 2 supplies and large control over the center of the map).
1- King's Landing:
March +1 on Dragonstone, March +0 on Shipbreaker Bay, Support on Kingswood.
Classic opening move, netting you a big and quite defensible stronghold to expand later over the inland. Consolidating power for 3 tokens every round from the very beginning is a big advantage over the other houses in the mid game, forcing Tyrell in particular to have a strong grasp on the Reach to try a raid or a march.
Move a ship in Blackwater Bay, then knight to Kingswood and footman to grab King's Landing (you can move your units in any fashion you like, but moving to Kingswood is better if somehow Tyrell doesn't go for the Reach).
March +0 on Dragonstone, March +1 on Shipbreaker Bay, Consolidate Power on Kingswood.
A less aggressive and well round set of orders which let you gain some power to dominate an eventual early Clash of Kings and potentially net you a Round 2 Blackwater and King's Landing.
Move a ship in Blackwater Bay, move Knight and FM to Crackclaw Point. Try to steer Tyrell away from the Reach in the early Rounds to ensure a quick and nice expansion, otherwise you may have to wait for a Mustering or have your plan delayed.
3- Muster/Sea aggression:
Special consolidate on Dragonstone, March +0 on Shipbreaker Bay, Consolidate Power on Kingswood.
As you hold the Iron Throne at the beginning of the game, the likeliness of not having a mustering on round 2 is around 66%; therefore ending the first round with only a stronghold may be not that crippling.
Move either one or both ships to Blackwater Bay, then muster a ship in Shipwrecker Bay and a footman in Dragonstone (or even 2 ships if you feel the need of a big naval presence from early on).
If somehow Stark or Martell didn't put their march +1 on the ship, you can capitalize on their error by moving both your ships in the adjacent sea and then mustering another 2 in Shipwrecker Bay. This way you'll gain a big tactical advantage over your opponents, having the opportunity to strike over huge areas of the map. It will also almost inevitably lead to a full-scale commitment by your neighbor to push you back and probably also an alliance against you, so weigh your risks.
4- Sea aggression:
March -1 on Dragonstone, March +1 on Shipbreaker Bay, March +0 on Kingswood.
If you totally want to expand north or south on the sea you can gamble on Stark or Martell using a special consolidate in the first round, giving you the opportunity to move last to use the march +1.
Move units from Dragonstone to Kingswood, then move your forces from Kingswood as you please, grabbing Crackclaw Point/Storm's End and sending back a footman in Dragonstone for later consolidate power. March in Narrow Sea or East Summer Sea, if occupied you should win at the cost of blowing Stannis (or Renly if you march with both ships hoping in a round 2 mustering).
If both Stark and Martell play safe and put 3 march orders, bad luck: move the ship into Blackwater Bay and try another time.
A note on going south: savvy Martell players can hold you out of East Summer Sea by playing Arianne Martell and then mustering ships from Sunspear. You may partially counter this by using Melisandre or Brienne killing their ship, or play safe if you fear the Red Viper.
5- Early Blackwater:
Special Consolidate on Dragonstone, March -1 on Shipbreaker Bay, March +0 on Kingswood.
As said The Blackwater area is paramount for controlling the center of the map and doubly useful for Baratheon as it hold two supply barrels. This opening sets you up for a quick expansion in round 2 while betting on not having an early Clash of King.
Move both Ships into Blackwater Bay, move FM to Crackclaw Point while leaving a PT in Kingswood. Muster a FM and a Ship from Dragonstone.
In round 2 support from Blackwater Bay and move your troops around to get both King's Landing and Blackwater.