Do I have to switch to Time Warner Cable business class?

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Hello, I am a college student starting a learning project. I have created my own web server and plan to host my own websites to learn and grow with. The account that provides my internet is not mine, it is my grandmother whom I live with. I eventually plan to add services like Google advertisements and maybe even start a small online partnership business using PayPal to make a little income. I was wondering if I would have to upgrade our service to a business class package? I do not believe that I would make a substantial income, but more like a hobby and learning experience. Thank you for taking the time to help me with my question.

I tried asking TWC themselves, but unfortunately they played the "pass the hot potatoe" game, and ended up at a dead end. And its a Sunday so I cannot call. Im sure they where just busy or something. :3

P.S not really a category to put this under...
Yes thank you Rein! I actually have quite a few ideas, and I actually have made some pretty good looking functional sites before that alot of people liked. The question was more or less just about the upgrading accounts. This is just my first personal in-home server and I thought maybe the IRS or Cable Company might have fine line between hobby and business. I don't believe I will be making something that will eventually be handed over to a family member trying to start up his online clothing brand.
I meant I will be handing it over eventually :3