UPDATE:
So after trying a beaded rope and a vinyl rope, I settled on this one which I like very much:
Danskin jump rope
I had to shorten it somewhat to fit me, but that's how they intend it- it comes 9' (which is long enough for someone 6'2") and you get to shorten it to suit you. I removed the weights from inside the handles for now. It is very sturdy and has a nice weight to the 'rope'. I had to unbend the fold kinks from it and sort of work it straight. Hanging it on the wall helps that too.

I think this is going to work for me! After a few days of stumbling about and stepping on the rope by accident every 5-10 jumps at first, I am getting better at it each day and find this to be rather fun now! The less I trip up the rope, the more fun it is. Holy cow though...it REALLY gets your heart going! I still have to do 20 second mini-rests every 30 jumps or so.
This is something that is easy and quick and fun for me to do a couple times a day as I pass by the rope hanging in the laundry area, maybe 100 jumps each time. As I build up my endurance I hope to do about 300 jumps in one session, maybe every other day. I know this will be excellent for preventing bone loss in the future.