Try out subdl[1]. It can work out the correct subtitles to download (based on a hash of the movie file apparently) and usually works well for me. I used to do this process manually but since trying out this tool I've been able to rely on it >95% of the time.
Don't assume the subtitles provided by the paid service are good quality. I've on a few occasions been unsatisfied by the subtitles provided by Netflix, and checked out subtitles from other unofficial sources to find these are much better. This is especially true for foreign language subtitles--the translations Netflix has is really poor quality for some shows and much better ones can be found elsewhere. One excellent example of this is the German show 'The Same Sky' which has terrible English subtitles that actually makes the shows unwatchable. The only consistently good thing about Netflix subtitles is that the timing is more or less correct.
Not sure about other streaming service as I don't generally use the others much.