I'm allied with Spain from the start of the game but avoided royal marriage because last time I became a vassal that way. Spain was pretty much my barrier in every war against France and Venice. I didn't want to conquer any part of Europe but I slowly annexed Morocco, stole Sicily and Tunis but those were more for fun than function.

I colonized Cape Verde first and used an advisor to increase colonial range. I started colonizing pretty early, my first set of ideas were exploration (after that I focused on trade and military because I was expanding fairly fast).

After Cape Verde I think Rio Grande was in my range and started expanding around that area downvards.

I sent conquistador to middle America and after my naval range was enough another one to North America and just started conquering savages.

By the year ~1650 England and France took a chunk of North America but I managed to setup dominant colonies in rest of Americas and Caribbean.

Mostly when I started noticing other colonies I'd set up mine right net to theirs and block their expansion. Grouping them to start creating states also helps because states will expand on their own.

On the African continent I just took Kongo and colonized Madagaskar to increase naval range and took few provinces of India and China but I don't see much point in those besides having bases there. Having colonies near Australia is cool because of spices but I colonized those quite late.

I like the the area of Mexico, Panama and Caribbean colonies the most because they seem to be a bit isolated and surround the Caribbean trade center which seems to be more and more lucrative. I recommend colonizing Caribbean as fast as possible because those parts seem to be full of sugar and tobacco and seem to be priority for AI.

If I was to do it again I'd prolly focus more on trade and expansion than military, maybe navy. Most European wars were almost completely naval (with trade CB) while for colonization you don't need a very advanced army.