Have you been to Maine Running Company? They do a good gait analysis and can help you figure out what shoe is right for you.

Don't know how much you run or walk overall, Sandra, but it does sound like (from your profile) that you're ramping up a bit. In my experience, and from what I've read, shin splint problems don't often come from shoes, more from just sore muscles and heavier use of increased miles, and/or from overstriding. You'll get 100s of opinions, many conflicting, and lots of folks' experiences if you post about your challenges in the Health and Nutrition section of the general forums. Don't hesitate to try to different shoes to get to what you like and what works well for you -- it can be expensive to zero in on your best match, but once you're there its a good thing. Personally, I don't like heavily cushioned shoes and use firmer models most of the time. I rotate between a couple different models of shoes to keep my feet entertained, and favor some for longer runs, some for shorter runs, and there's one model I've been using lately in all my road races (they give me blisters, but they feel fast...and I need all the help I can get) -- point being, there's not always one shoe perfect for all the times.