Ranma's used to dealing with hard people while training, Betsy wouldn't be all that different from people back home to him!

Any of those three sound really fun! Heart Break Hotel and Closing Loose Ends are right up Ranma's alley since fighting's his bread and butter (leaning the former more but I'm completely down for the latter too), and at the same time... he's a shounen protag, he likes to eat and can eat a lot of cheese.