I really like the diva cup and have used it for several years now, once you figure it out it's like nothing and makes a monthly inconvenience barely noticeable (if you're lucky and don't have bad cramps).
When I first got it I put it in before I got my period so that I knew how to insert it and take it out before things got more complicated. You'll find the best way to insert that works for you and the best way to remove it, if you need me to be more graphic let me know haha, also there are entire menstrual cup forums where you can post your problems/questions, it's amazing.
I find it leaks when it's over-full, so you will learn how often you need to empty it, and yeah it can be difficult to manage in a public stall at first which is again why I recommend practicing at home. I have re-useable pads that I use as a liner (and that sounds gross but seriously they are so easy to wash and I love them, I got mine from here:
http://hyenacart.com/stores/TreeHugger/), and that's it, no more disposable pads and no more tampons, which seem so uncomfortable in comparison, I would never go back.
You could try the instead cups one month to see if you like the general idea, they're disposable and a little different to insert (easier) but I have used them and liked them too.