It seems to take forever and a day for me to get the infrastructure up and running before I think it's time to start another city.
Is it just me, or is that normal for the rest of you?
I don’t think that’s normal.
For my part, in turn 135 I have a dozen cities and already a small solid army.
You must have a production speed problem in your base colony. Here’s my advice:
your first city must be dedicated to politics: you must place your units in the order: lumberjack/ carpenter/ farmer/ statesman then Preacher
Rule #1: Use specialists.
For buildings it is in order:
Village hall / dock / pier / chapel / village well (buy it to save tools) / Town hall / Lumber Mill / City hall etc.
Once consolidated, you can make a forge and possibly 1 or 2 industries, but that’s later in the game.
Then for all the following cities:, it is the same beginning lumber jack/ carpenter/ farmer / production ; production dependent on resources (cotton/tobacco/etc.).
For the buildings of the following cities it is the same but you rush the industry according to the available resources:
Village hall / dock / pier / chapel / village well (buy it to save tools) / production / Town hall / Lumber Mill / upgraded production / industrie 2 etc.
To make this second city you’ll have to buy units at the immigration dock in Europe. To have money, the best is to have scouts (indispensable: seasonned scout !!), 2 or 3 minimum. Otherwise trade in raw materials (bought from Indians). The production/sale of raw materials in the colonies can also be a solution but it is less efficient.
It is the scouts who will allow you to raise money quickly (and it will bring plenty of other benefits. I have already posted it, it is the most important unit in the game. You need Jacques Marquette.). All the first treasures they will make appear must be sold to the king at 50% to either recruit specialists or saved for the first gallion.
Edit: and of course get at least 1 pioneer asap to build 1) roads 2) improvements *needed*
That’s the beginning. Good luck and good game!