When I was mobile and home based I had two of everything, I'm so forgetful it was easier to have everything in both places. In fairness this was pre gel polish so no huge expense and cumbersome lamp. I think if I was still doing it I'd have two lamps too, the one being transported is vulnerable to damage so I'd want a back up, the salon one would cover that too.
I carried about 10 polishes but always checked what colour they wanted in case they wanted something specific. I always called/text the day before to confirm appointment and it was part of my pre planned conversation along with parking, lighting, sockets, table, seating, etc.