From my just finalized Spain game, which is the first game of EU III I've played through to completion. I think I did pretty well. I wanted to play with the colonization stuff, so that worked out.
The goals were to unite Iberia, form Spain, and then turn my back on Europe while building a colonial empire in America. I ate Grenada, then formed an alliance with France which covered my back in Europe, and secured the northern border. Ate Portugal, and Aragon. Expanded into Morrocco for the Barbary Pirates Defeated modifier, and to give me something to do while waiting for Azores/Canaries/etc to core. Enacted the settlement policy in North Africa to seed Castillian culture in one province, and by game's end I had pretty much assimilated all of my african provinces.
I then colonized like crazy, and let Europe do its own thing. By the time I popped up back in Europe, France had been overrun by Burgundy, which was in turn overrun by Austria, and then France was balkanized into a bunch of warring kingdoms that took turns becoming variously ascendent, and then stomped by Austria. That's when I started nibbling. A Guyenne here, a little Dauphin there, some Brittany for dessert; it all worked out pretty well.

Did Fabricate Claims on Naples/Ferrara/Sicily, and inherited them all in one shot, so I then worked on acquiring more Italy, and linking it up to France. Did some minor expansion in Asia (Ceylon) just to get the Indian trade modifier.
Went full Narrowmind/Mercantile/Aristocracy/Free Subjects/Naval/Defensive, and stayed Catholic. Took CAD as first idea for Gilded Iconography, and kept it all game. Never realized what a good NI that was. Early cultural tradition for top advisors, and ridiculously low stabilization costs. With an empire that big, I was recovering a point every two months; bring the comets on!
What do you all think about this one? Next game I'm going to try Oman I think; I want to try different mechanics like trading, and westernization. Any tips, or good AARs anyone can recc? Thanks in advance.