What your town builds first is a matter of opinion and strategy, so it's hard to say which one is always the right choice. Here's some information that may help you in your decision:
This allows your town mates to go into a place with huge trees and all work together to chop them down. You will get plenty of resources (logs and sticks) which can be used for a number of things.
If you build this first, your town can use all those logs and sticks to quickly fill up warehouse crates and get gold every day.
This building enables town chat and creates an activity log that shows who spends town gold, cancels building progress, takes items, uses machines, etc. This is a fantastic tool for towns who want to coordinate their warehouse and effectively be the leader in the town assessment.
If people are eager to build up their houses, they might want this sooner rather than later. The lumber yard lets you build planks which are necessary to upgrade your house after level 3 and you can only get them from the lumberyard. It takes logs to build 1 piece of lumber, though, so that's why sometimes people do logging first.
The only function of the Bank right now is to buy town Gold with real money. This is useful if you or townmates know you'd like to purchase gold to speed up the progress of your town.