I too am mobile, I use this floor cover
PVC Protective Floor Covering 132cm x 150cm Black its think and nonslip so very durable. Make sure its tough enough to withstand wear on original floorboards without puncturing (depending on your clients houses) and textured so its non slip!!
I also have a portable backwash its a sibel deep back wash which I ONLY use at my house if clients come to me. I tried it with a bin at first to collect waste water, its so messy and was a pain. So with some modification of the basin hose I have been able to connect it to the waste under my kitchen sink (where the washing machine connects to). For the spray hose (i have a mixer kitchen tap) I had to buy a garden hose to tap connector and then bought a shower head and hose and connected it to the garden hose connector which fits to my tap. over all Its great for washing off colours but there is no way I would dream of taking that to clients houses, it would take too long to set up and the time involved means you are their longer. Most of my regular colour clients come to me for colour and if just cut etc I go to them.
If I do have to go to a clients house for colour do it in their kitchen. I use the side/work top for foils etc and I make the client move the chair around so i can switch sides to reach colour or foils. I stand my tool bag this one (
Lotus Equipment Carry Case, Beauty Tool Carry Case ) on the worktop and place my back mirror standing up in front of it which works well for checking haircuts.
Other stuff I carry are a 3 meter electric extension cord (in case your not near a plug socket) small dust pan and brush, extra towels and lots of plastic bags (for wet towels, used foils waste etc)
Also, if you are in the UK you could join the Freelance Hair and Beauty Federation which makes you look professional and they also do insurance too. They have regional groups so you can meet up with for training etc and makes you feel like you are not on your own/for advice etc this is the link
http://www.fhbf.org.uk/index.php
Good Luck!