I don't carry anything while I'm off duty. I used to, but I outgrew it.
While on the job I only carry a few select items:
Pen (usually 3 or 4 because I always lose them)
Stethoscope (Because I don't know where the ears of others have been.)
Shears ('cause ya never wanna have to tease your rookie partner for carrying them, then have to borrow them on the very next call because you don't carry them)
I also have a "Go Bag" that I take on long flights. It includes:
Additional cold weather gear. (Snowpants, parka, big mitts, facemask, 'cause, you know, it would suck to survive a forced landing only to freeze to death.)
A small survival kit with fishing line, fire starter, etc ('cause, sometimes, ya just gotta fend for yourself.
Couple bottles of water and a few granola bars, ('cause, you know, it would suck to survive a forced landing, stay warm, and starve to death.)
A good book. ('cause, you know, it would suck to survive a forced landing, keep warm and nourished, yet die of boredom.)
As for what the station will provide, it varies from one company to the other, you should check with them.