Brody and Sophia are not fans of stairs (so I'm of no help in that department).... both of them can easily jump up onto and off of the furniture. I do my best to stop them and try to just lift them up. Brody actually likes to jump OVER the stairs onto the couch.... silly boy.
Congrats on the new apartment!! When I moved, I made sure to revacuum the new apartment just in case something was missed. When we started moving the items, I kept Sophia crated in the bedroom of the old apartment I constantly came back, took her out of the crate for bathroom breaks & played with her. I didn't want her going crazy with all of the coming in and out of the apartment! We did the move in one day, so it wasn't so bad. After that, Sophia was the last thing to pick up and go!! Good luck