Hello Chantal -

A p-value is a function of sample size, and even if it were usually more directly interpretable, which it is not, there are various ways they may be distorted in multiple regression.  Such a statistic can be misleading. 

It may often be a better idea to pick your model based on subject matter considerations, and then see how well it performs on test data.  You may also want to research "model selection," and "model validation."  You could compare performances of candidate models.

You might also consider graphical analyses, as in Figures 5 and 6 in https://www.researchgate.net/publication/313925533_Comparing_Model_Performances_Graphically

When comparing model performances, beware of overfitting.

Interaction terms could be left in perspective models, or taken out for performance comparisons. 

Cheers - Jim

PS -  Also, you might need to decide if you are interested in explanation or prediction.  An example shown in the appendix to the following by Galit Shmueli, may be instructive: 

 https://www.researchgate.net/publication/48178170_To_Explain_or_to_Predict

Further, there may be a number of good books which might be useful to you, such as

Applied Regression Analysis and Generalized Linear Models, 2nd ed, 2008, John Fox, Sage  

Method Comparing Model Performances Graphically

Article To Explain or to Predict?