I used to travel on bus/tube (London - no car at that time). I used to have a Samsonite wheeled holdall that housed everything. This was easy (for me) to carry up stairs to top floor flats, and wheel about town. Inside that I had a catty bag with brushes, products, clips, scissors etc so you just pull that out and plonk on their dining table/worktop and stand your back mirror up against it. Then it was just developers, dryer, tint bowls pre cut foils etc in side compartments, colours were in a plastic klip it container and floor mat/ tiny dustpan and brush just on top. For me this worked best, it was organised and easy to get to something quickly. I looked professional with a decent black holdall on arrival and it wasn't obvious why I was going to someones home (some people liked that, especially the ones who were "working from home"). Once the clients became regular I refined kit down a lot so wasn't taking all of that every time. If it was just a cut and blow dry I would just take a messenger bag with necessary tools/products/towel etc.