"Is it true that long distance running will slim the legs, waist and hips?"
I wouldn't narrow it to distance running...or even running. Cardio will slim the legs, waist and hips. Running, however, is top on the list for cardio. There is a reason...it is hard...or it can be hard.
I wouldn't recommend jumping right into running to my worst enemy! Start by following a beginners program and start doing a run/walk (there is zero shame in it, I have friends who complete entire marathons this way with impressive finish times).
Running is very hard on your body, joints, tendons, ligaments, skelatal system. You must start by easing into it because the risk for injury is high. It's high impact and there is a lot more to it than most people think (your own body mechanics, etc.).
Wendy aka fitmom started running last year or so and eased into it beautifully! I am sure she'd be willing to share tips, if she hasn't already.
If you have been doing Cathe step for a while, you have a good head start. The impact of the step aerobics will make a running program easier.
As for clothing, stay away from anything that has even an ounce of cotton. Grab "wicking" fabrics (it will specify on the tag), I like polyester.
HTH!!