Your first bill will be larger than your normal bill since it will include the full amount for the coming month, plus a prorated amount for the portion of the partial first 'billing month cycle' that you had service.
It doesn't hurt to call and ask where the bill is at. And while you are at it, find out what the estimated first bill will be.
I have learned that TV and Internet service might be on different bill cycles. It also has to do with what your "Due Date" and "Serice Date" are. It may take 2-3 bill cycles to 'settle down' as well.