This is an important point in the game. Many people have wasted their free upgrade by using it on the wrong building. You will not be able to upgrade more buildings until level 17, and not until you create enough hardwood and marble to do so. You need to upgrade the building that will benefit you the most. Things to consider are the cost of placing the building and what resources you run low on the most.

These are some suggestions for your first upgrade:
Fisher: once this building is upgraded you can start buffing it to increase production. If you find yourself low on fish to create buffs, this is a good choice.
Storehouse: Are you always running out of space? Upgrading your storehouse will give you an additional 400 spaces for inventory.
Copper Smelter: Do you find yourself running out of bronze? This upgrade could help keep up with the needs of the tool maker and the bronze weapon smith.
Tool Maker: Always waiting on tools, or having to use up resources to create them in your provision house? Upgrade this building to increase your tool production.

Not Recommended:
Fir Wood Cutter, Forester and Sawmill: These buildings are very cheap to create and can be torn down later if you need more licenses.
Well: Very cheap to create, and will eventually run dry and need to be replaced.
Residence: Once you can create the Noble Residence you will most likely want to delete all of these and replace them to preserve you licenses.
Bronze weapon smith: While this may seem like a good choice at first, it can quickly use up all of your available building licenses. Once bronze weapon smith needs 4-6 resource buildings to keep it running (1-2 copper smelters, copper mine, 1-2 coking plants, 1 fir cutter). An upgraded bronze weapon smith needs a minimum of 8 resource buildings to keep it running smoothly.

Please feel free to add any corrections, suggestions, or other opinions to this thread, I am creating this section for a guide and want to make sure it is accurate.