If it's not a hassle to bring extra snares and cymbals, do it. Better to have it and not need it than to need it and not have it.
You may want to check with the studio in advance to see if they have a house kit. Of course, we'd all like to use our vintage gear, but if their kit is dialed in, it will save time. If time is wasted, let it be on account of someone else. I recorded a few months ago: I had a set of Slingerlands in the car, but the studio kit was fine for what we were trying to do.
Here are the most important things:
For you, make sure any gear you bring is in tune and in working order. Oil moving parts (pedals especially) and seriously consider fresh heads.
For your band, have a plan and be well-rehearsed. For a one-off session such as this, the studio is not a place for practice or jamming. Be aware that the engineer may wish to track final vocals separately, so time spent on basic tracks cuts into the time for overdubs.
Despite all of the above, relax and have fun. Don't overthink it: it should be like a successful rehearsal, except with a bunch of extra mics.
Al