With the cleats, think about your riding style and how much walking you might be doing as well before purchasing pedals and shoes.
SPD’s. (The ones your probably mentioned) are two screw metal plates with pedals that can be one sided (normally with flat) or dual sided. They are mostly looked at as gravel / mtb ones but I would recommend these if will be walking more or just tootling along rather than exerting with speed. Go for ones with a wider platform for support as the smaller cleat area can cause hotspots on your feet. The cleats are normally recessed slightly on most shoes.
SPD-SL’s are more for racing and the cleats are exposed more. They are normally three bolt ans made from durable plastic, but will wear more with walking, plus awkward to walk in anyway. Go for these if wanting more performance.
As you are going defy which is more endurance then speed, I’m guessing the former is the ones you need.