I have just bought a Peloton bike but have my own shoes with SPD cleats. Are there any specific pedals I should buy that are compatible with the bike.... or can I switch with any pedals that have spd cleats?
Congratulations Gaby and welcome to the cult of peloton! Yes, you can use any SPD pedals. Just make sure they're SPD and not SPD-SL assuming your cleats are SPD. If you expect to have people using your bike who may use sneakers rather than bike shoes with SPD I would suggest dual platform so the other side is flat. Here is one option - there are many cheaper versions out there.
If you haven't changed pedals before, do it carefully, use grease and you'll need a pedal wrench, etc. If it's not in perfectly and you crank it you can mess up the threads on the pedal and the crank.