Snowbyrd as for ice and sport climbing there are only few things are similar or crossover. I think where sport climbing transfer over the most is in mix climbing and steep aerated ice, where it is more hooking and balance. Hooking is placing your picks on ice or rock rather than swinging them, it is like reaching for a hold and placing your hands in the right postion to grab and pull on that hold. Ice climbing is a love hate thing, either you hate it or you love it, and if you love it there will be days where you hate it. Most women I have met hate it, just because of circulation issues trying to stay warm, but that shouldn't discourage you because there are a lot of women who do enjoy the sport.
For the most part poeple gradually transition into climbing ice. Most start on lower angle slabs and some people take years before actually getting on vertical terrain, besides toproping. In rock climbing a vertical wall can be easy to quite hard, in ice vertical terrain will most always feel hard. as suggested already the best option is probably taking a course where they will have all the equipment you will need and you won't have make big investment right off the back. Or find somebody that you can borrow gear from, but that is usually quite difficult to do.
To prepare for ice climbing I hit the weights in the gym, get burly, you'll need it. I usually start with 20-30 minutes on the stairmaster to start off. Then I do dumbell simulated tool swings, LH swing 10-15 overhead using the mirror to try and swing into the same spot, then RH same thing, repeat each arm3 times and do three sets, it will give you a good burn. Pulldown 3 sets of 15. Tri extensions on the pull down 3 sets of 15. Arm raises front and side 3 sets of 15. Bicep curls 3 sets 15. Row for a bit and then hit the stairmaster again. I try and do this regularly for 2 months prior.
Most people will say the ice sucks here, I have had only one season here and New England was way better, but there is ice around here to climb, and the weather is much more forgiving here. Good Luck.