Sid Meier's Colonization/Industry

Eventually, your main products should be lumber, ore and food. Everything else is just cash. The only thing you will be paying for instead of building locally are free colonists (600 gold).

Producing a bit of all cash crops is more profitable than specializing in just one - the prices aren't going to fall that quickly and the king won't have that strong threat.

Do not keep large sums of gold in treasury (500 is a large sum of gold in early game, 1000 is a large sum in mid/late game). Invest everything - buy ships (Privateers, Merchants, Galleons), tools (at least until you can produce enough), colonists (immigrants early, from the Royal University later). A few units of Artillery may be useful, but their prices rises too fast, so it's better to build you own. Frigates cost too much, as do mercenary armies from Europe (if you're even getting such proposals it means you aren't investing your money fast enough).

Don't forget to seed every colony with 2 horses. Horses are important for transportation of colonists and for raising army. If one of the colonies has too many horses, put 50 or 100 on a wagon train and transport them somewhere else, so it can keep producing them.