What the previous poster said as far as kid sizes. Also, unless something has changed the 2 year old doesn't need a ticket so they don't need a magic band unless you just want them to have one. But if you do by all means, DD loves hers and likes wearing it around the house sometimes, and now that she's a little older we let her.
I also would not trust a child that young to wear one by themselves. We got one for DD when she was almost 3 and then we went on another trip when she was 3 and a half. She would 100% have lost it because she would have wanted to take it off to wash her hands, adjust it, "look" at it, etc. Instead we carried hers in my pocket and when it was time to tap in at a ride, if there were not people waiting, we would hand it to her and let her hold it up to the scanner. Same thing at the room, it became her "job" to open the door at the resort whenever we got in and that suited us just fine.
At the time the 50th anniversary statues were around and we would also hand it to her if we stopped to look at those so she could wave it and trigger some of the interactive stuff. I think the only time she actually wore it was in Haunted Mansion after the stretching room because she noticed ours were glowing and pulsing and she wanted to experience that too. Once we were in the carriage it went right back in my pocket.