Indeed. In general, you have more bargaining power when you unite all of your coworkers in one union. But it may be strategically wise to begin with a department where mutual understanding among coworkers is high; once you've got the union up and running, you can help coworkers organize and join.
All the resources I found say you need 30% of the employees at a company to organize. Do you have any details about how this works at the division level?
Close, but that's not quite right - 30% is the threshold within a "unit" (which can be one department) for a "showing of interest" which can be used to trigger a National Labor Relations Board election. An election is one of the most common ways to get an employer to live up to its obligation to bargain with its employees, but there are several. For an overview, check out "Labor Law for the Rank and Filer" by Daniel Gross.
Legalities aside, if you want to organize a union with your coworkers the first step is to form an organizing committee that is broadly representative of the unit you are trying to organize. You can then either form an independent union, or join an existing one. I'm happy to answer further questions by email (which you can find in my profile).
When workers don't have democratic organizations of their own, their interests fall by the wayside.