Overview:
Baratheon is a dynamic house with a lot of options for getting your 7 castles. You can go after lanni/tyrell, starks or martell for the win. Supply is usually a deterrent to your conquest so securing blackwater or even mountain of the moons is critical after getting kings landing. Keeping shipbreaker and blackwater is an absolute must and the rest is up to you.
Track Influences:
You should aim for a balanced position in all three tracks with an eye towards being higher than any of your potentially hostile neighbors on the iron throne. This becomes important in the situation of who attacks first and raiding. If you can maintain iron throne holder, this will be important in deciding tie-breakers for allies and enemies alike. If you aiming to embark on a sea conquest to take starks or martell sea, then having good position on fiefdom and kings court becomes important to break through.
Consolidate power at dragonstone, and if possible assuming you can counter-raid other people's raids, at kings landing and kingswood. However, assuming you can get blackwater & /or reach, you can support from kings landing.
Opening Moves/Priorities:
Your priorities should be in the following order: 1) Securing blackwater and shipbreaker 2) Securing kings landing and 3) Securing blackwater or mountain of moons. Keeping shipbreaker and blackwater
The safest opening is the following:
Kingswood - Consolidate Power (CP)
Dragonstone - CP Special Order
Shipbreaker - March
Move both ships to blackwater and muster 1 ship and upgrade 1 FM to KN (if equal mustering). If there's no equal mustering, it's safer to muster 2 ships into shipbreaker in case Martell is aggressive attacking from the sea. On the 2nd turn, secure kings landing with knight but make sure to have one FM in dragonstone to ensure constant CPing at dragonstone. On the third turn, aim to secure blackwater or go north, south or west if opportunities present itself.
If martel or starks does not have a march +1 on the sea, you can consider taking the sea but it means you cannot take kings landing or possibly secure supply.
Alliances and Game Dynamics
As you in the middle of everything, you can potentially have a lot of enemies and friends. As you can best fight one enemy, is best to pick your spots and make unnecessary enemies. If greyjoy is fighting lanni, take advantage and grab blackwater in return for lanni alliances. If greyjoy is fighting starks, take mountain of moons in return fo starks alliance. As you the iron throne holder, use that to your advantage to secure favours and such. If martell is hostile to you, make sure to have starks alliance and do not
Note
One weak point is storm's end. Martell can muster a ship into the port and either raid your defence or support or attack from there. A raid from shipbreaker can easily solve that problem. Another problem as noted is that martell can use arrianne to kill your one ship on shipbreaker and take shipbreaker if he has a double march on ESS and port.
Generally speaking, i ensure i have 2 ships on blackwater bay and at least 2 ships in shipbreaker to ensure a solid defence at shipbreaker. This is also eats into your 3-2-2 supply making getting blackwater or mountain of moons critical.
Support System:
As long as you have shipbreaker, you have unraidable support from blackwater bay to protect your main lands and shipbreaker. If you can secure blackwater and reach, you also put a 2nd unraidable support around kings landing too. Even if you only have blackwater but not reach, u can put a support around kings landing provided you higher on the iron throne and can raid other people's raid first.
Potential Directions:
1) Go West and attack lanni and tyrell for their lands
2) Go North and attack starks, narrow sea will give you access to moat, white harbour and eyries. Getting Shivering, will give you sea domination and additional access to winterfell
3) Go south and hit martell. Taking East Summer Sea ensures access to storm's end (which you can already access), sunspear and starfall. If you can take sea of dorne too, then it'll ensure sea domination but harder to do.
4) A bit of everything, maybe take harrenhal and reach if lanni/tyrell are busy fighting others, then take narrow sea/east summer sea to access the last 2 castles.