Departure from Tampa - What time to arrive and other questions

We are on Brilliance of the Seas, departing Tampa at 4:00 on 3/28/15

What time would we be able to get on the ship?

What time would you recommend arriving there?

Any inexpensive but clean hotels nearby? We will be driving down from NC, so we are not sure whether to come down the night before or to just leave early in the morning.

I'd arrive at 10:45am to 11am. They usually start boarding between 11am and noon.