I personally prefer to go to a rented salon/rented room within a hairdressers etc.
However I do have my own home salon but I went mobile first and then took the clients to the home salon. However most of them wouldn't follow me as they sought me out specifically because I came to their house.
However I would beware of going mobile to start with because clients always seem to think that as you are mobile you should charge less, when actually the reverse is true as you have to use petrol to get there, spend time driving and setting up etc which you are not getting paid for!
I'm hoping to start renting a desk soon in a new salon and can't believe how much I've had to hike my prices up to cover my rent, but I think people will pay the big bucks in a nice salon. The ambience in most people's houses is awful-it can be a nightmare trying to do a spa pedi with screaming kids and pets running around the place!
Good luck with whatever you decide!