I would like to add a little bit to the previous answer. The way BU works, is that we have a top level BU. This is often referred to as the Parent BU. Nothing can be added above it. So this is advisable to consider this an Admin BU and refrain from building campaigns etc in this one.
So in your case, you could create two child BU's under the parent BU. This will keep your BU structure flexible. You can change the hierarchy under the parent one at any given time.
You would need at least 3 BU's including the one that comes with a Pro or Corp edition of Marketing Cloud. The Enterprise Edition includes 5 BU's.
Speaking of data, given the way Marketing Cloud handles subscriber data, ALL subscribers that are added to what we call the All Sub list, will be visible in the parent BU.
So you mentioned that the two teams work separately and data should be kept separate from the two teams, thats fine in the Child BU's, but if you are the admin, you will have access to all subscribers as part of the All Sub list.
The advantages of working this way, is that you as the admin, can use the calendar feature on the admin level and get an overview of all the Child BU's campaigns etc.
There are other numerous advantages to this model, but I hope at least you got a bit more info in order to make an informed decision.