Each filter you need is essentially a stand alone unit, with an input and its
own output, so you would not connect them in series unless you make
cascaded sections for a specific frequency and want steep slopes which
implies higher order filters. Normally cascades are done with second order
sections, and in this design case you do connect in series. Note the tool
generated this solution, but its not practicable due to order way to high.
Here is an example for your 100 - 1000 Hz filter with steep slopes -
If the order of this filter was only 2 or 3 then a cascade would not be necessary, but you would not
get the steep slopes as shown above. Also the order of the above filter way to high for analog
solution, as cumulative errors of passive values and drift. "Normally" 6 - 8 second order sections
limit of cascaded opamp filters.
Digital filters can do very high order, here is one with much steeper cutoff characteristics -
Another approach is comb filter design which are simple but images have to be removed.
Regards, Dana.