Sarah, it's great that you are getting interested in bowhunting and archery, but I have to warn you, once that archery bug has bitten you are addicted for life.
As far as bows go that package seems like a good package and diamond makes some nice bows for sure. I personally don't like packages because I'd rather pick out my own accessories. Most manufacturers make bows with short draw lengths and lower draw weights to fit kids and women so you should have no problem finding one to fit you with a little research. Your best bet would be to go to a pro shop if you have one near you so they can properly fit you with a bow.
Is bowhunting better than gun hunting? Not necessarily. I enjoy both for different reasons. If I had to choose I would choose bowhunting, but I know many that would stick with the gun. Either way, a day in the woods is a good day.
Good luck and keep firing questions out as they come up as we have a great bunch of guys/gals here that are more than happy to help.