As adult skaters with bigger bodies, we typically need more support than the kiddos. So, while Jackson Artistes are rated for beginners, they're rated for beginning children, which is why you likely don't feel sturdy in them. I wear Jacksons too, and based on my skill level, I should wear the "Premiere" boot. But, I've got a big booty and a few extra pounds and would break those down in an instant (I wear the Elite 4500s instead).
I don't think that using the Artistes is a bad thing and they certainly won't make you fall on your backside. However, if you think you're going to stick with the lessons for a while, I would invest in a sturdier boot. You'll likely still feel uncomfortable on new skills (we all do!), but the support will be better in the long run and it should make new skills easier to learn.
Hope that helps!