For starters - welcome to home automation. You will find SmartThings less painful than your prior experience I think.
On your washing machine, the motion you want to detect is vibration, not motion in a room which is what most motion sensors detect. I don’t know of a vibration sensor that is ST compatible but I’m guessing there may be one out there if you google for it.
[EDIT] - this thread has some ideas:
On the cats, pick up an pet-sensitive motion detector. Facial recognition is beyond the scope of ST’s abilities and overkill for what you want to do. I use EcoLink PIR motion detectors and they are pretty rock solid and do a good job of ignoring small pets. They do pick up my dogs but they are as big as people. Should work fine for your cats.