First War - India
In order the get the Thirteen Colonies to join you they will ask you to capture three settlements. You will want to do this fairly quickly but war with France is not a pleasant prospect and the Cherokees are tougher than they look. Instead you should begin by heading for the Eastern theatre. Take virtually all of your armies on the British Isles and board the fleet. Send your forces to India and attack the Mughal Empire. They are incredibly weak and ripe for the plucking: you should be able to sweep through Northern India very quickly.
Kill the Pirates
It is worth while hunting down the pirates and destroying their fleets once and for all. You will probably need to combine all your starting ships for this. They also hold an island settlement near Port Royal which you will need to take for victory anyway and they are quite easy to beat in a land battle. You might find the pirate fleet a bit more challenging but destroying it will prevent them from hassling you in the trade theatres.
General Development
You should build schools and trade ports when you get the option because schools will allow you to research more technology and trade ports will bring the cash rolling in. If you manage to establish some spare trade slots then try and get new agreements with other countries. They will be resistant at first but you can persuade them with gifts if you feel it is worth it and it often is. Keep an eye on your government members as well, watch out as they develop good or bad traits and take action accordingly. If you reduce taxes for the middle/low class you will grow faster and new towns and ports will spring up. Try to ensure you spread your gentlemen throughout your schools as they are more likely to have an impact that way than if you stick them all in the same one.
Diplomacy
It is best to avoid being dragged into any continental wars during the early phase of the game. Try and get alliances with Poland or Russia. Avoid Prussia because they always fight with Austria. You ideally want to stay friends with Austria until they go to war with France and that way you get the opportunity to declare war on France without Spain joining in. Later on you can drop Austria as an ally because they keep trying to drag you into wars.