It depends on what kind of filter you are talking about. If it is a wound (particulate) filter or a carbon block filter or combination of both then it really doesn't matter as these don't effect mineral content (I assume you are contemplating a mineral only test such as the popular Ward Labs tests that so many on this forum have done). If the filter is an iron removal filter then again it doesn't matter unless you pick a test which measures iron. You would, in that case, want to check input and output to see if the filter is doing its job. If a neutralizer is involved then again, both input and output should be checked to see what effect the neutralizer is having on pH, alkalinity and hardness. With softening an input only check will do as softeners are so effective that you can take the input hardnesses (as CaCO3), divide by 50 and multiply by 23 to get the additional sodium (add to input sodium) and call the output Ca and Mg hardnesses 1 ppm as CaCO3 each and be very close though again input and output tests confirm proper equipment operation. If an RO system is involved check TDS as suggested in #4 but test at the input.
In general, test at the source coming into the house. This will give you the best picture as to what you have to deal with. In terms of what to enter into a brewing spreadsheet, for example, given only any input test, you can assume that your on line equipment does what it is supposed to. The exception to this might be the neutralizer. Easy solution there is take it off line when you brew. This makes sense as all it does is add alkalinity and a bit of hardness and except in rare cases you don't want any more alkalinity than you are already stuck with. In those cases you add controlled amounts yourself.