We started out with _http://... and quickly setup _http://www... (which we redirect to _http://...). A month or so ago, I finally get the SSL cert setup for our domain and now everything is automatically redirected to _https://www....
(1) Should I add all variants? (2) And should I set the https://www.domain.com as a primary?
There is quite a bit of traffic (hehe compared to what?)... ~15,000 unique users per day.
Keeping the variants apart from the one you're using is redundant, keep one set and you should be good to go.
Have you already added all the three variants? I too had sites that have gone through the same process, we even had two properties in webmasters (one with www and the other without) - soon discovered that if we had 302 redirect setup, we had no use of the older versions.
BTW: 15k unique visitors is a pretty decent amount, hope you get more :)
Cheers!