Most supply everything, but you can get a better stethoscope at a toy store than the ones they usually have.
Make sure if you use items with batteries such as coagulation monitors, O2 sats, blood glucose monitors that they provide you with those batteries.
Have seen a few nurses use a sewing box for a nursing bag, which works pretty well, easier to see and get what you need as opposed to digging in a bag. Most of the company supplied bags look like diaper bags.
A little bit late, but I used to carry my own bathroom scale. Surprising that some people don't have their own scale at home. It wasn't anything fancy - like it wouldn't be for very overweight pts, or those unable to stand ...
The company should supply everything. Our cheap company doesn't supply pulse ox's though. They have pretty good supplies for a good price on Amazon and some bags too. They usually give you a cheap diaper-bag like thing that isn't very user friendly. Get a washable one or a wipeable one anyway because some homes can be kinda nasty.