What do we do if SETI is successful?

For a somber, deeply intellectual view of what could happen, I can't recommend enough Stanislaw Lem's His Master's Voice: https://en.wikipedia.org/wiki/His_Master%27s_Voice_%28novel%...

"Given that our civilization is unable to assimilate well even those concepts that originate in human heads when they appear outside its main current, although the creators of those concepts are, after all, children of the same age—how could we have assumed that we would be capable of understanding a civilization totally unlike ours, if it addressed us across the cosmic gulf?"

Me and my dog cannot talk.

I understand my dog and he understands me.

If they experience death then we have massive common ground already.

And you are comfortable being the dog in this cosmic relationship then?