Good running/jogging shoes work best. It's best to get properly fitted at a running specialty store, like another poster suggested. You can walk in running shoes but walking shoes are heavier than running shoes. So for your long walks you can use your walking shoes and for walking/jogging/running you can get a pair of running shoes.
I wouldn't avoid an occasional jog just because you don't "have the right shoes". Running shoes are expensive. And unless you know that you enjoy running and you're going to take it up and do it more seriously and keep at it, running shoes would be a very expensive thing to buy on a whim!
It's perfectly fine to use your walking shoes for a short time. Occasional jogs, and deciding whether you want to incorporate running into your regular exercise schedule now, is fine.
But if you do decide you like running and want to keep doing it, yes, some good running shoes are a very good investment.
Fitness Minutes: (79,213)
5/6/12 3:02 P
Many sports have a number of necessary equipment. Running or jogging is one sport in which you only need good running shoes. It is way cheaper than many other sports. It would be good that you have a running shirt that can help transport sweat without getting wet, similar running shorts etc, but these are not essential, because you can make do with conventional cotton apparel. The only essential equipment are a good pair of running shoes, you can't make do with anything less.
Fitness Minutes: (15,905)
9,717 5/6/12 1:47 P
I honestly don't know about occasional jogging, but I do know that if you're going to run/jog, you need shoes designed for it. I've had cross-trainers, and any running at all is seriously hard on them, and wearing the cross trainers puts strain on my ankles and shins.
If you can afford it, I would definitely have some properly fitted (As in, go to a specialty store to be fitted) running shoes.
My BFF recently bought me new walking shoes since I do a lot of charity walks. I went for a long walk today and felt like jogging for awhile. Are walking shoes okay to use for jogging occasionally or should I get jogging shoes?