Season 1: Are there any benefits in completing the game beforehand?
Tomorrow Season 1 will begin and I want to start with a new character then.
I'm currently playing a Rogue at Level 50 and I am at Act V. When I play through the game before starting Season 1 with a new char, does this make a change? Can I skip the story completely after completing the game once?
Finishing the campaign unlocks the campaign skip for new characters. Seasonal characters will not be able to access seasonal content (malignant hearts, extra story, etc) until the campaign is complete or skipped... so unless you feel like playing through the whole campaign again, you'll want to complete it with your eternal character first.
From what I've heard, yes, by completing the story once on your account all (inc. seasonal) characters are able to skip the story entirely.
There are also some account-wide benefits like the shrines, and apparently they were considering making map exploration stick - though I haven't seen that confirmed.