Unless you own something that is related to the G&E or Camera department and the production company asks for it, for example, the two Alexas, a camera operator doesn't have to bring anything at all.
Just make sure that you have a bag with a your rain gear, some clean clothes, a pair of socks and very good and comfortable shoes.
As extras I would say, bring a girdle (I use it all the time), good gloves, towels and knee pads as Luiz suggested.
I have a Mark V director's viewfinder in the bag but I have been using Artemis or a normal PL director's viewfinder as of lately to set up the shots.
On the operating side, make sure that you don't see any lights, flags, frames, etc in your frame.
It sounds easier than it is but as a b cam operator you have to make sure that you don't upset the cinematographer while setting up the shot, and sometimes either the cinematographer or the director will ask for things which can't be done because of one of them so you have to be super polite.
Like: Follow the actors! and then sometimes you can't because if you follow one actor he / she could be wrongly lit or you might end up catching a flag.
One of the best things that a camera operator can have access to is "assemblies", if you can see what the production is getting from your camera, it will help you be less stressed and your skills will improve by the minute.
Stretch for 10 minutes and use a tennis ball on your back for 5 minutes first thing in the morning, will save you from getting injured on the back.
If the show is going to be hand-held, put the camera down as soon as the shot is finished, this is very important, you only have one back and you want to keep it.
Leave all things camera related to the 1st and 2nd, it is going to be difficult because you will want to make sure that the Preston is connected right, that the card is inserted ok, and those things that people from an AC background think about when operating (like myself ) it will take time but once you stop thinking about technical things you will be more focused on framing in a better way.
In my opinion don't get the Alexa Mini because the viewfinder is one of the worst viewfinders ever and if you are going to spend 12 hours looking through one, I would choose the Xt's viewfinder over the Alexa Mini's one anytime.
By the way, if you want to keep your eyes forever, reduce the brightness in the viewfinder your eyes will thank you for that later on.
Have a good day.