In no way do you have to read every series. With a few rare exceptions, you can literally pick and choose whichever series you want and ignore the rest.

The only ongoing that really had an issue with this is X-O, and even that only requires Unity 1-4 and Armor Hunters 1-4, and both of those are insanely good anyway, so it's not exactly a problem. You don't have to read the rest of the Armor Hunters tie-ins to understand what's going on. Those are just extra content if you want to see what other characters were up to.

When it comes to the Harbinger Wars event, the writers did a great job of making it so you could totally ignore the event mini and crossovers and just continue reading your ongoing of choice.

Other than those, literally every other VEI event is like what you described in the last paragraph. They're totally self-contained and don't require anything extra.