My tips for the Greyjoy's;
Do not spend any of your starting money on the kingship claim, or buildings, just recruit troops, (ironborn warriors and raiders).
You should have enough troops to have two near full stacks, put some of the generals together, you will need them all to fight, not govern!
Attack and capture Seaguard first, it is rarely defended well, then the next term sack it, and destroy all the buildings. Move that army north and take The Twins.
With your other army sail over to the Lannister coast and sack the closest undefended settlement there.
Bring your first army down the Lannister coast as well, sacking and destroying towns all the way down (you may not want to sack each city in order, the AI rushes troops to hotspots, so just get back on your ships and sail further down the coast, you can come back for that settlement any time!)
After you have destroyed the Lannisters on their own coast (I left Casterly Rock untouched as it was consistently garrisoned heavily) then move down the coast towards the Tyrrels.
Promptly sack Oldtown and all the other surrounding tyrrel cities and castles. If you want to hang onto the Arbor thats fine, it may be used as a springboard for further conquests.
At the start, never hold any cities on the mainland, only islands, as you can not hope to face armoured knights.
If you have played your cards right you should now have about 100,000 monehs!!! I did exactly this and got this amount, oh and i didnt fight a single battle myself, only autoresolved! This stupid AI!
From here, what i did was send one army back up towards home, sacking sacked cities as i went, to start a war with the northmen, the other kept travelling around the contenent (sacking as they went) to attack the northmen from the other side of Westeros.
Even though the Greyjoy's say "we do not sow" it is still a good idea (when you have enough) to invest in farms, the little money they get you is not to be scoffed at! Also when you are offered the sellsword guild (you have to have over 10,000) get it, the heavy horse that you get eventually is very helpful when invading the continent for good, and the spearmen are nice for bringing down those self righteous knights! And build a bigger fleet, always build a bigger fleet!
That's about all really, happy plundering!
Oh and i played on hard, just so you know