The Philosophy of Science

You want some guidance on pursuing study of Philosophy of Science (I take it you mean natural science rather than social science or economic science). Such a subject is only part of any degree course. It was part of my B.A., (Maths and Philosophy) and my Ph.D. qualifying exam (Logic and the Methodology of Science) included it. There are good reasons why it needs to be studied in tandem with other things. For example, it has proven very difficult to distinguish science as an epistemological activity from other such activity. Attempts to identify a distinctive “scientific method” that reliably leads to knowledge have so far generally failed (there was a lot more hope 80 years ago than there is nowadays). It makes sense to study Phil Sci along with a science (for example you can study Maths & Philosophy, or Physics & Philosophy, at Oxford; Medicine & Philosophy makes sense), or along with the History of Science (much Phil Sci indeed looks at the history), or as part of Philosophy more generally.  

I am also a strong advocate of combining study of such disciplines with developing practical skills - the accompanying science in the <science>&Philosophy courses above; economics or finance for business; accounting; medicine & health; IT; engineering of some sort. Too many young people finish a 3-year or 4-year degree course without having obtained any specific skill that they can offer in exchange for a salary. That is OK for some, but manifestly not for all.

You want some guidance on pursuing study of Philosophy of Science (I take it you mean natural science rather than social science or economic science). Such a subject is only part of any degree course. It was part of my B.A., (Maths and Philosophy) and my Ph.D. qualifying exam (Logic and the Methodology of Science) included it. There are good reasons why it needs to be studied in tandem with other things. For example, it has proven very difficult to distinguish science as an epistemological activity from other such activity. Attempts to identify a distinctive “scientific method” that reliably leads to knowledge have so far generally failed (there was a lot more hope 80 years ago than there is nowadays). It makes sense to study Phil Sci along with a science (for example you can study Maths & Philosophy, or Physics & Philosophy, at Oxford; Medicine & Philosophy makes sense), or along with the History of Science (much Phil Sci indeed looks at the history), or as part of Philosophy more generally.  

I am also a strong advocate of combining study of such disciplines with developing practical skills - the accompanying science in the <science>&Philosophy courses above; economics or finance for business; accounting; medicine & health; IT; engineering of some sort. Too many young people finish a 3-year or 4-year degree course without having obtained any specific skill that they can offer in exchange for a salary. That is OK for some, but manifestly not for all.