I am not a lawyer nor was I an English major. However.........
The first clause, "subject only to the police power," modifies the second clause, "right of the individual citizen...." It essentially negates it. One does have the right to keep and bear arms in Illinois, but since that specific right is subject to the fancies and faddish whims of the police power, it basically renders your right a mere privilege, subject to "the police power." It is the old proverbial "rights versus powers" argument.
In my opinion, rights are something you are born with, humanly recognized and God given, if you will. Powers are something that is man made, and delegated to other groups, individuals or entities. Powers are privileges. But in this contemporary topsy-turvy world, such terms are meaningless and often largely determined by those who are in charge and maintain the heaviest firepower, and hence, the largest physical and legal influence over the common citizenry. (That is why prohibiting semi automatic rifles from the general populace is so important to these various types of odious people)
Owning a gun and ammunition in Illinois is a privilege, whether you choose to believe it or not. However, the 10 Amendments to the Federal Bill of Rights supercedes State Constitutions in that regard. Most people would disagree with me however, but the fact remains that the Constitution & the Bill of Rights is the supreme law of the 50 states.