One thing you will need to think about as you put your board together is how much space you will allocate for the different aspects of your project. You want your board to be easy for a judge or someone else to read, so the font needs to be big enough that someone doesn't have to squint and can scan easily. That also means that things like the background investigation needs to be considered carefully. If the information is meaningful, you need to include it. For example, you might want to add background research or thinking if it:
1. Explains why you chose this project or the method.
2. Gives information that someone else needs to know which explains the science behind your project.
3. Explains the importance of your science project to a real-life product, problem, or situation.
The short answer is that the background research is essential for you to design your project carefully, and you will need to have that information in your notebook. However, you don't need to put it on your board unless the person looking at your experiment needs to know it to understand or appreciate what you have done.