Each level of building can only be built once a certain level of Population has been reached. This is not usually a problem as by the time your ready to build it the Population has reached that level, and there's always something else to build. The bigger more complicated building require a higher Population, but then there's no point building them unless you have someone to put in them.
Build a Lumbermill First
As a Lumbermill increases Carpenter efficiency by 100% it is best to build it straight away so other buildings can be built quicker. There is usually an over supply of Lumber from land clearance and Petty Criminals (it's about the only job they are good at!), so the Carpenters must be efficient. A Population of 3 is required to start the Lumber Mill (2 would be better, for one Lumberjack and one Carpenter with the Colony square providing enough food for 2) - this is not too much of a problem as a Soldier or Pioneer can be temporarily moved in to increase the Population.
The only exceptions to building a Lumbermill first are a Stockade which can be bought if the Colony comes under attack if you go to War, or Docks if the land can not provide enough food, partically if there is a Fish Square near by.
Next Build Building that don't require Tools
New Colonies will not have a Tool Making Industry, so they will have to be shipped in at first. So it is a good idea to concentrate on building those buildings that don't require Tools, while you await supplies. These are given below [with cost in Hammers]. Note excess Hammers over this number are wasted, so either hold back some Lumber temporarily in a Wagon Train, or bring some in from a Wagon Train to fill Carpenter Capacity during the last turn of production to optimise production.
Lumbermill  - hopefully already built.
Stockade  - build this first if there are hostiles in the area. Remember once built the Colonies can NEVER be abandoned, so don't build in temporary Colonies eg. Silvermine. Increases defense by 50%.
Armoury  - allows you to build Muskets, and Artillery, note you WILL need Tools to build these but it is good to have it ready incase you need to rearm quickly. Muskets can be traded at a BIG profit.
Dock  - if Food is running low or you have a Trained Fisherman this can be useful.
Schoolhouse  - if you have a lot of untrained Colonists build this, remember the extra Teacher required may upset the Sons of Liberty Ratio.
Warehouse  - if goods start piling up build this QUICK, note a second (and final) level will require an additional 20 Tools.
Stables  - if you have any Horses in the Colony this will double their breeding rate, this is subject to Food availability, only half of the excess (rounded up) can be used for Horse growth. Breeding rate further increases with the size of the Herd. Once you have 300 Horses breeding stops until you move some.
Church  - good for Blessing Missionaries to go and pacify local Indians AND get rid of one unskilled Colonists. DON'T put a Preacher in there or you will be buried in Colonists, and your Country will end up like poverty stricken and unstable Brazil, as opposed to the more prosperous and productive United States.
Wagon Train  - build this to transport goods from the Interior, and bring in Tools, Muskets, and Horses. Remember you can't have more Wagon Trains tahn Colonies, unless you Capture some.
The order which you build these is up to you, and depends largely on current circumstances.
Next Build Building that require few Tools while your building up your Tool Industry
You will probably only have 100 Tools to start with (1 Cargo Hold and the Maximum a Colony without a Warehouse can hold). So this gives you 5 lots of 20. The following building only require 20 Tools, [hammers given in square brackets]:
Blacksmith's Shop  - once this is built you can start building Tools from Ore, so never sell any Ore the Indians give you, just save it up. If you are down to your last 20 Tools build this, or if you have none your can still make a few Tools slowly in the Blacksmith's House.
Tobacconist's Shop , Weaver's Shop , Rum Distillery , or Fur Trading Post  - if your producing any of the Raw Materials these require build them, particularly if you have a Skilled Worker to put in them. It's a good idea to build them all anyway as Indian Gifts and Pirate Plunder can be manufactured into more Profitable Goods, and sold in Europe, or back to the Indians. Also, when you get Adam Smith you will be ready immediately to build Factories.
Warehouse Expansion  - you may wish to have all Wagon Trains go to a central Port where raw materials are manufactured and shipped to Europe. In this case you will need the maximum storage space while awaiting ships bound for Europe, or Raw Materials to be manufactured. Also if you are blockaded, have a large Horse Herd, or are close to Pirate attack points it can be useful. No further expansion beyond 300 is possible.
Printing Press  - Sons of Liberty is critical to the Game partically at higher levels, so as soon as you get some Tools in build this.
Buildings requiring 50 Tools
Magazine  - doubles Musket production but requires double the Tools. Useful in a Colony with a lot of Ore.
Drydock  - allows Ship Repair. Thus preventing a lengthy return to Europe, and increasing the Chances of breaking a blockade due to being able to come out quicker after repair and the ability to lore enemies into the Colonies Fortresses Artillery Range.
College  - useful for bigger Colonies. Increased skill level of education, and allows 2 teachers to teach.
Newspaper  - build this as soon as you can to increase Sons of Liberty Membership, remember to keep a Statesmen in the Townhall to maximise it's effect.
Buildings requiring 100 Tools
Fort  - increases defence to +100% and will fire on enemy ships in neighbouring squares. Very useful, reduces defender loses, build it when you get a chance, or straight away if at War, or if troubled by Pirates.
Shipyard  - allows all types of Ships to be built, only build in a Lumber Rich Colony as ships are very expensive to build. You might be better of just buying Ships from the King as their price remains constant.
University  - allows ALL skills to be taught, and allows 3 teachers to teach.
Cathedral  - increases cross production. I would NEVER build this except that it keeps appearing on the production menu and irritates me, so the only way to get rid of it is to build it. You require a population of 16 to build this (not the 8 stated in the game documentation) so will have more colonists than you can use by this time anyway.
Buildings requiring 200 Tools
Fortress  - the last word in defence. Has better firepower against Ships, and +150% defence. Keep a Wagon Train handy as it is difficult to build this without either having a Tool shortfall which will cost you money, or overload which will be thrown away.
Once you get Adam Smith you can build Factories
Note you will need to have built the previous level of Manu'factory' first. All commodity Factories cost 160 Hammers, and 100 Tools each. They increase output by 50% at no extra cost in Raw Material. An Iron Works costs 240 Hammers, and 100 Tools having the same effect. This may cause an overload of Tools if not properly managed. The Arsenal Quadruples Musket production combined with the Magazine and costs 240 Hammers, and 100 Tools. It does not however increase efficiency, due to the already increased efficiency of the Iron Works. So if you build it don't keep it permanently manned or your will run out of Tools required for other things and get an overload of Muskets.
Once you get Peter Stuyvesant you can build a Custom House
This costs 160 Hammers and 50 Tools. This will automate trade in the Colony even during the War of Independence. Once you start building Factories you will really need this due to the increased level of goods, and reduced profit per item.
"Max Out" Colonies
If you have no immediate need of Military or Transport Units get your Colony to build every building available. They increase productivity and defence and cost nothing to maintain. Thus once all building have been built you can just pour out an endless stream of Military Units and steamroller your enemies. No choice between Guns or Butter, it's just Guns, Guns, Guns... This also allows newer smaller Colonies to concentrate on buildings. This will make for a slow start but once production gets under way you will be unstoppable, as the computer never builds everything. If there is a Military shortfall Units can be bought in Europe.