Before you start writing...
I suggest you look up Bob Silverberg's "Up the Line", which explores these themes in exquisite (and hilarious!) detail. Every theme in this thread is there, time tourism, unauthorized and criminal temporal joyriding, meddling with history, forbidden vacation getaways in the past, and a Crucifixion so crowded with time travelers that they outnumber the participants. Add the usual time travel paradoxes and misguided attempts to correct them, and you have a perfect send-up of the whole genre.
In my circle of friends, the book was so popular that whenever any one of us disappeared for a while, he was said to be "Up the Line" (in the past).