All three have a specific use but once you understand the difference they are easy to use and master.
'Motteimasu' is used for things that you're holding as well as general items that you own, either tangible or intangible (i.e. personality, belief, etc.) but stops short when talking about living things. That said, you may run into examples that contradict what I'm saying here. It'll usually be a case of the sentence being a weird exception or wrong.
Watashi ha kaban wo motteimasu. "I have a bag."
'Katteimasu' is used for ownership of a pet.
Inu wo katteimasu. I own/have a dog.
'Imasu' is an existence verb for living things. If used after a person, 'imasu' will use "ga," but if it's after a location, it'll take, "ni."
oneechan ga imasu. I have an older sister. Kanojo ha heya ni imasu. She is in her room.