>>1400882new pedals generally come with cleats
you can buy cleats separately as well
there are road (3 bolt) shoes and mtb (2 bolt) shoes
road shoes can use any road system and mtb shoes can use any mtb system
the most common ones are spd-sl and spd, the shimano road and mtb respectively
both are good systems
don't let casuals tell you that spd-sl is too hard to live with and don't let dentists tell you that spd isn't good enough for road riding