When you purchase a set of Shimano SPD pedals new, they come with the SPD cleats you will need.
Then you have to find a pair of riding shoes you like that are compatible with SPD cleats, and there are LOTS of those made.
So while you can just use regular tennis shoes until you find the riding shoes you want, you will need to purchase a pair of SPD cleats once you do purchase shoes to use the pedals as they were intended.
For me, shoes are a very important thing. Good shoes will feel good, look good, and last for many years. IMHO, don't go cheap when you buy your shoes and make sure they fit correctly.
I'm thrifty, ( read that as cheap **** ) so I went around to local bike shops and tried on shoes till I found the kind and correct size I wanted. Then I went shopping on the internet and found those exact shoes for $40 less and bought them.
Maybe some of the other folks that know more than I do will comment, but I say good shoes are one of the most important pieces of clothing you will purchase.