I paid $30 a month for a 500cc and now pay $35 a month for my fzr600. For reference my car insurance is $50 a month. (all liability)
If you're looking for sportbikes I've enjoyed my FZR and they can be had for $1500 or less. (Also, I've got parts if you need them
) Other bikes like the CBR and Ninja will probably handle better, but it won't matter that much for a learner bike. Otherwise it might be smart to start with an older bike or something less sporty. I had a honda cx500 that was dead reliable. I've heard good things about the yamaha 650 specials. Both are early 80's bikes and can be had relatively cheap.