You want a contract. Without one, you’ve got no recourse if you show up one night and they say, “Gee, it’s slow tonight so we don’t need you,” or “Season’s over. Bye!”.
A deposit isn’t usual for a steady, at least not that I’ve ever heard. You might do one day so they can see for sure that they want you, but then you should get a contract with some kind of notice clause (for both sides), unless you are as skilled as a friend of mine is at getting restaurants to agree that he only shows up if he hasn’t got something else better that day. (I wish I knew how he gets them to agree to that.)
I’ve usually done a 4-week notice clause in the past, and I used to figure pricing based on my two-hour minimum for three or four hours. In other words, when I was charging $250 for a two-hour casual, I’d do a three hour brunch for that.
However, everything is pretty weird right now, so I’m not so sure that any of this applies anymore. But you do need to consider the situation where they may suddenly make a change and you’ve turned down other jobs because you expected to be playing there.