The truth is, ain't no easy answer.
The best shoes for ME are probably NOT the best shoes for YOU.
Furthermore, the top rated shoes listed in Runners World, probably would NOT be the best shoes for me. When it comes to shoes, there is no easy answer, no quick fix. If you walk into Dick's and grab a pair of the rack because they are pretty, you will most likely end up with either shin splints, sore knees, or a stiff back. You'll hate running. You'll quit and then say, "how can you DO IT?" If you are making a commitment to become a runner, you must take the time to get properly fitted for shoes. Be committed to make the time and spend around $100.
Ask around for a good running supply store in your area. Here in North Texas, Luke's Locker is THE place to go. When you go, tell them that you need to be fitted for running shoes. The person fitting you should watch you walk in your current shoes. They should watch you walk barefoot and run barefoot. They will be looking to see if you pronate. Or not. People with pronation issues have feet that sort of roll in when they walk and run. This can lead to extremely sore legs and knees. Because so many people experience this, shoe manufacturers now make antipronation shoes.
They should evaluate your instep and arches. Try a few pairs of shoes on your feet. Again, with each pair they should watch you walk and run. Your running shoe should be roomy. Not at all tight. You don't want to feel your toes on the tips of the shoe. When standing up, looking down at your feet, you should be able to see the sole of your shoes.
(In this picture you can see a white edge on the outside edge, or bottom in this photo, of the shoe. That is good.)
If ANY part of your foot hangs over the sole of the shoe, the shoe is too small. Try again.
You may need an arch support. Don't grab the one on the rack at CVS. Ask your shoe fitter if they'd recommend one for you (this varies based on the model of your shoe and your foot) and what support they recommend for your shoe. Try the arch support ON in the shoe in the store BEFORE you leave.
Once you've found "the shoe" I recommend running on a treadmill to really assess the shoe. A good quality running store will take back a worn shoe that wasn't properly fitted. From that point, if the shoe works and you love it, there's really no need to be fitted again, unless you choose to change your model. I've been running in the same shoe model since I had Isla. Before that, I was in the same Brooks for 2 years. If it ain't broke, don't fix it!