Based on this picture it looks like you can use the Shimano SPD cleats. You can get these which are multi-directional release, meaning it's a bit easier to get out of the pedal since you can release the cleat from multiple directions. These are great if you're new to clipless pedal systems or know that you want to be able to quickly and easily release. You could also get the lateral release cleat. This cleat requires you to laterally engage your foot/shoe to release the cleat. This can be popular for folks who really hammer down on their pedals, might be doing a lot of high intensity intervals or climbing, or doing spin classes because there's less potential to accidentally disengage your cleat by pulling directly up off the pedal.
This pedal style will work with any cycling shoes that have a two hole pattern on the bottom of the shoe. Mountain Bike shoes like this would work, as would any shoe with a 2-hole cleat design. Any shoes with a 3-hole cleat design (often labeled as "road" shoes) would not work for your pedal/cleat design without an adapter.
I hope that helps, and Happy riding!!
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