Distance between star systems

I'm writing a story that will eventually escalate from being focused on one planet to the entire star system that planet belongs to, and finally to a big story involving the two nearest star systems to the one the Original planet is located in.

So what I would like to know is what is the minimal distance these different star systems will have to be apart from each other? (I don't want them so close as to be binary star systems but the 3 different systems should not influence each other with gravitational pull either)

P.S. If it matters what type of stars we are talking about, if we call the Original star system A and the others B and C then A has a Main Sequence Star (basically our sun), system B has a Blue Supergiant, and system C has a Red Dwarf.

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Distance between star systems

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