I'm waiting for our MSF course to buy a bike, but I'm still keeping an eye out and seeing how much I need to save

So far I'm leaning towards a ninja 250 as everyone seems to love it as a beginner bike. The nimbleness and light weight would work well for my wife and I, and being able to keep up on the freeway is a big help. I really have no desire to ride a sportbike, but since the seating position is much more standard, I think we'd prefer it over a laid back cruiser that doesn't maneuver as well. I'm hoping they have one at the MSF course we can try first...
My only concern with this bike is that it has a fairing, which I understand is really expensive to replace after one of us inevitably drops the bike.
What I'm wondering is, can I just remove the fairing until we get the hang of things and are less likely to drop it? Other than looking stupid, is it safe to ride without it? Do they come off easily?
Seems like it would be wise to get the easily broken piece of plastic out of the way for the first few weeks, but I've never heard about anyone doing this...