You have established your first colony, and now the question is what buildings to finish first. Obviously, in order to build anything at all, you need to assign a colonist to the Carpenter's Shop and make sure you are chopping lumber or have some lumber stored from clearing forests. It is essential to start building as soon as possible, so bringing in an Expert Carpenter should be of high priority.
One often tends to plow the Colony field, and this will get you some lumber to start off with. Expert Carpenters are much more efficient than any other colonist working in the Carpenter's Shop or Lumber Mill, but often times a Free Colonist, Petty Criminal or Indian Convert can do the job of cutting lumber until you get an Expert Lumberjack. In addition, Carpenters are more expensive than Lumberjacks, so buying an Expert in Europe and then educating new Colonists to Carpenters will save you some money.
You only need a Schoolhouse to teach the Carpenter skill. If you have few open student slots in your educational facilities (which is often the case early on), choose to teach the Carpenter skill before the Lumberjack skill for the simple reason that Carpenters are more expensive than Lumberjacks.
The Lumber Mill
Now on to the buildings. Which buildings to choose is of course subject to circumstances, but the obvious first choice is the Lumber Mill, because once you have the Lumber Mill production speed of new buildings will double (if you have enough lumber).
There may be a few times when you have to prioritize other buildings, for example: You are producing a lot of fur and need to store it somewhere. In this case maybe you may need to get a Wagon Train first. Or, perhaps you get a Fisherman early on and are eager to make use of a Fish Resource off your coast -- in this case you may want to start building Docks.
Sometimes you only have two colonists in your colony (you need three to build the lumber mill), and if this is the case, Wagon Train or Docks are good options.
Try to avoid unnecessary buildings
Some buildings don't have much use early on. A good example of this is the Warehouse. Sure sounds great to have all that extra storage capacity, but wait a minute? A Warehouse costs 80 hammers and gives you an extra storage capacity of 100 (for all cargo). A Wagon Train, on the other hand, costs 40 hammers and gives you an extra storage capacity of 200. If you are in need of 100+ storage capacity early on, it probably means that you are producing a lot of one cargo type, for example fur, and with a wagon train you can now store up to 300 fur for the cost of 40 hammers instead of 200 fur for the cost of 80 hammers.
You also have more options with a Wagon Train:
1) Cargo stored in Wagon Trains are safe from boycotts -- they won't be thrown into the sea. Storing Tools and Trade Goods in Wagon Trains is therefore a smart strategy.
2) Wagon Trains can be moved around. When they aren't needed in a colony, move them on to another colony where they are needed or use them for trade missions.
Build a warehouse when more cargo types are starting to pile up -- this usually happens a little later in the game. The main point is to focus on the buildings that benefit your colony in its early stages of development.
Suggestion for building priority
1. Lumber Mill >> Doubles the efficiency of your Carpenters
2. Wagon Train >> Allows you to store 200 extra cargo: good if you are producing a lot of one cargo type early on and good for storing extra tools/trade goods. Can also be used for trade.
3. Schoolhouse >> In Colonization, time is of the essence, so make time work for you by starting education early.
4. Printing Press >> You should have been able to get some tools by now, and the Printing Press requires 20 tools. Liberty Bells are important to increase rebel sentiment and getting those Founding Fathers quickly.
5. Colony Specialty Building >> Depends on what the colony is going to produce. Fur Trader's House, Tobacconist's Shop etc.
6. Let circumstances decide from here on. Lacking Tools? Maybe now is a good time for a Stable (no point if you don't have enough food to take advantage of it), or a Church if you are playing as England and want to fuel immigration. Remember, though, that those unskilled colonists can be blessed on the Docks in Europe, so you don't need to build a Church for that purpose. Maybe a Warehouse could be wise at this point. If you DO have enough Tools, though, a Newspaper could be a good option.
You need enough Tools in order to produce Muskets and Artillery. It could be wise to assign one of your Tool Colonies to produce muskets. Here's an example how: Establish two tool-producing colonies. In one of these colonies you then build an Armory (and later a Magazine and an Arsenal). This colony can now switch from producing Tools to Muskets depending on what you need at the moment. If you are producing Muskets, but find yourself in sudden need of more tools, simply move the Gunsmiths over to Church duty or just fortify them inside your colony until they are needed again.
Colleges and Universities
You probably don't need Colleges and Universities in all your colonies. Make some of your colonies education centers. For example: Assign one colony to educating Veteran Soldiers and one to Elderly Statesmen. You could give them names to describe their purpose, for example West Point and Capitol Hill. Then one colony for planters etc, and some scattered schoolhouses for farmers, fur trappers etc. Two or three universities should be sufficient, after all, they need a good influx of new colonists ready to be educated.
Once you have a Factory in place, goods will start piling up, so it's usually a good idea to have built a Warehouse before you build a Factory. After the factory is completed, you may want to expand your warehouse capacity or begin building a Custom House.
It's a good idea to build your first Custom Houses in junction colonies, and then bring in cargo from surrounding colonies. Later, as your colonies become more productive, try building Custom Houses in all of them to ease the logistics process -- moving all those Wagon Trains tests your patience after a while.