I don't have any experience with altitude sickness, but I think it's unlikely that a few days in Medellin before going to Bogota would make much of a difference. All things considered, I would do Bogota first so that they can adjust to the temperatures. Bogota will be only slightly warmer than Seattle in March, Medellin will be Spring-like weather and then Panama will be brutally hot.
I will make a couple of suggestions in case you had not thought about them:
First, you will want to remind the students that Bogota can be chilly at night. It gets down to the low 40's in March. Many people think that because they will be near the equator they won't need jackets or sweaters and pay the price. Heck, I've even made that mistake and shivered for two hours during a late-night layover in BOG.
Second, inexperienced travelers often shy away from South American airlines because they are unfamilar. You may want to tell your students not to be afraid to book their flights on either Copa or Avianca, as that will give them many more options than if they try to stick with USA-flagged carriers. Connecting on COPA in Panama is very easy.