Beware!!! I am not a lawyer but remember these things ..

The F1 visa is an international student visa in the US. The F1 is issued strictly for the purpose of studying in the US, and the F1 visa holder is legally required to leave the country upon the completion of studies.  The Green Card is for the permanent residency (immigrant) status, with which the holder can stay in the US indefinitely pursuing whatever he or she wishes.

You have already noted, in a way, that your plan of action - applying for the green card and being in a the F1 - are in conflict. The F1 student visa, stipulates that you must leave the US upon the completion of your studies. Thus, your intent must be that of staying in the US temporarily.  As a result, you can not have the intent of staying permanently in the US (as required for the green card) and, at the same time, have the intent of staying in the US temporarily as required for the F1. If you pursue both plans, the only impression you would communicate to the US INS (Immigration & Naturalization Service) is that you are not being truthful, in which case both applications will be rejected.