It's free! As long as you're not using it for hours upon hours upon hours you should have no problem with Verizon. Even if you use it daily for multiple hours at a time I haven't heard about Verizon hasseling anyone. Welcome to root and enjoy the new phone you now have!!
Also, I don't know which wireless tether app you've d/l'd but I highly reccomend "Wireless Tether for Root Users" I tried a few different apps before I was encouraged to try this and I must say that this one is by far the best and easiest tether app there is. Period, end of story