I can barely stand on a bosu ball, so I won't be trying that anytime soon.
Is it better (for beginners) to have an underinflated balance tool or a very firm one?
Yes, this is NOT the starting point, but it is very much in line with the guidelines for athletic training on the bosu. I trained directly with Douglas and Candace Brooks when I certified to be a master trainer...will be seeing him up in Vancouver in a few weeks (AWESOME person, btw).
Just curious...why would you say not to jump? We even have football players doing plyos on them, and the lbs per sq inch of pressure they created is much greater than any figure skater creates. It's certainly later in the progression of skills on the BOSU, but it's definitely something we do with a variety of athletes.
If you're just starting out, work with a firmer BOSU, and really start with some orientation and stablization work to help kickstart training of your vestibular system. I will post a video of this, since it's something I don't often see trainers and fitness instructors doing in BOSU classes, and it's very very important for success for more challenging activities using the bosu without injuring yourself.