Does incall or outcall always mean it is in a hotel? For example, could a newbie have a provider come to his/her place or meet at the provider's residence? If so, how much to set aside for a hotel in NYC?

Incall just refers to location relative to the provider.  "Incall" means that she stays in, and you go to her.  "Outcall" means that she goes out to you.  If her ad says "Incall or Outcall" then she'll do either one.  Generally, she'll charge more for outcall to cover her travel expenses / extra time.

In call can be anyplace the provider chooses. Most use hotels but some have apartments that they use strictly for work.  Others operate out of their homes though that is the rarest case.

As far as out call. Some girls will come to your place, some won't. Personally I think having them to your place is a bit risky but that's your call.

Hotels in NYC? Not cheap but you can save some money using Priceline and the "name your own price" option if you are a little flexible. I paid $150 for a room a few weeks ago but I have paid as much as $400.
Be aware that some girls in NYC will only do out calls to certain areas.