I'm a fan of less periods overall myself!!! not quite liking the age I'm currently at for many reasons, one of which is being on the pill is riskier so I stopped it and am back to being at the mercy of my hormones....sigh.
honestly I wouldn't worry much about the birth control choice. the increase in shedding is small.
I was on Depo and I planned on going back on it although my fiance has had a vasectomy I don't really need birth control I use it to manage my endometriosis pain.
the birth control pill has been found to increase shedding of hsv2 slightly. if you are taking daily suppressive therapy though, it's not an issue.