Think very carefully about booking the sectors separately.
Almost every time bad weather or something else delays a flight there is always at least one person on the flight that gets very upset because they are going to miss their connection or they will not have time to recheck their bags in in time to make their next flight.
I see it all the time and it is a false saving. Those checked through on one ticket get automatically booked on another flight if they arrive late but these people struggle to find a flight with any seats sometimes.