Cleats and shoes

I cannot correct you if you are wrong because I can't see your cleats. I assume you have 3-bolt cleats. Look also makes 2-bolt cleats, but that's not what they're known for.

Your cleats are probably compatible with Look Keo pedals; in addition to Look themselves, there are a lot of other companies making Keo-compatible pedals. Look has an older design called "Delta" that is not compatible with Keo, so if your cleats look really old, they might be Deltas. I don't think anyone is still making Delta pedals.

Note that Shimano SPD-SL pedals are very similar but incompatible; note also that Shimano SPD pedals are completely unrelated to SPD-SL pedals.