Currently increasing population and I´ve started to produce Tools.. Not weapons yet...
I'm all of one game ahead of you, so take this for what it's worth. It seemed to me that ore was next to worthless except to make tools. Tools were primarily needed to make guns, though some units and buildings require tools also. Both guns and tools were fairly cheap in Europe through all of my first game. The upshot is that it seemed largely a waste of time mining ore and making tools and guns. Better to use the colonists to work on high ticket items and their needed raw materials and simply buy tools and guns in Europe.
Perhaps the cost of tools and guns varies more at the higher difficulty levels.
Not to hijack your thread, but since you're generically asking about hints and strategies for beginners, I started my second game last night. In the other Civ games I've taken more of the get-along-with-the-neighbors approach to the early game. After reading some strategy tips here, when I discovered the Dutch just a bit to my north I decided to take a more aggressive approach. I invaded with my scout right after discovering them, waltzed right in and took a city and a hardy pioneer.
Then I discovered they had another city just a few tiles further north. Next turn I took that one.
Then I found the English just to the north of what used to be the Dutch territory. I took one city from them and razed another. Also captured another hardy pioneer.
Just a few tiles to the west I found the Spanish. Two turns later New Madrid was mine. Two turns after that I razed their other city. They took back New Madrid when their scout wandered back into town, but I quickly dispatched him and retook the city.
About this same time my ship sailed past a nearby island and discovered another English settlement. I loaded up my scout and sailed into town.
I'm just a small number of turns into this game and I already have more cities than I did in the entirety of my last game. I've got a system of roads connecting most of the cities and I'm improving the resource tiles to start specializing.
So, next time, if you bump into another civ early, send in the cavalry and take his city while it's wide open and easy pickings. It appears to be a great way to get a huge early start.