IT is all a personal prefernce issue. Do what you feel comfortable with and make sure you read up on how to carry/dispose of things properly.
I have polycystic ovaries. Depo is not an option because anything with progesterone in it makes the cysts worse and I take on water like the titanic. So far nuvaring and yasmin are the best on the market for getting rid of the cysts by stopping the ovaries from ovulating. I was on yasmin when I wasn't hiking and the nuvaring when I was hiking.
On a long hike when I knew I was supposed to get my period my doc told me to just switch my ring out and not take the one week break. Nuvaring has two forms of estrogen in it at doses lower than the majority of the pills....and its an insert ring and don't worry for 3-4 weeks.
As for other methods there is a great site to go to for female hikers....http://hubpages.com/hub/How-to-Hike-During-Your-Period