The Rover app itself can handle most scheduling needs (but it doesn't have time slots, yet) so a digital calendar or notepad can be useful if you have a number of clients. Weather gear, but this has been stated and will vary depending on your climate. I invested in some extra toys, leash, and an adjustable collar with my information on it for stays. I also totally dog proofed my car and added safety gear. I went the extra mile because I always have dogs with me but its totally things you'll want to consider if you plan on traveling with clients. If you're boarding be sure your home is dog-proof and have cleaning supplies!
I'd say the "necessities" are weather gear, a dog bowl (always offer water after walks), treats (opt for allergen free), poop bags, a few toys, and most importantly, a good pair of shoes if you're walking! I cannot emphasize how important that is! Stay safe out there!