This may need clarification. Some people refer to clip-in pedals as clipless. They require a cleat on the shoe and you clip in for a secure pedal connection. These can be a little problematic if nervous about unclipping when necessary. They represent an acquired skill. Most shoes made for clip-in pedals have stiff soles for a positive transfer of effort. More efficeient pedaling, but harder to walk in.
The other type of pedal is called a flat. It has sharp pins to grip just about any shoe. I recommend a skate-style sole for these (the most popular brand by about 10:1 is a brand called Five Ten). I will disagree with Mark who said any shoe will do. I recommend a shoe made specifically for mt. biking which will have a slightly stiffer sole and be much more durable where it needs to be. Flats are far more forgiving while riding, but will take chunks out of your shins or calves if they hit you unexpectedly (like when you put a foot down for almost any reason).
Do NOT ride mtb with the pedals that are on your bike in the photo. There is no way you will stay on the pedals when you need to, unless you attach old-fashioned toe clips.
Just say no...
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