I've done mobile, then was given the opportunity to rent space in a salon (in a different area to where i live) last year, but it didn't work out so I went back to being mobile, but i've just been offered a space for a nail desk in a local hair salon (which i'm still thinking about).
Best part of being mobile is you can choose your own hours, products, prices. But, unfortunately there are only a certain amount of clients you an fit in in one day (i.e. mine is 3 sets of extensions) because you have to add setting-up & packing-up onto your time, as well as travelling to and from clients house's (and dont forget extra if your travelling at rush-hour). Also you need to make sure people know you exist i.e. advertise.
If you rent a space in a salon, although tecnically you are your own boss, you have still got to work with the owners rules, and if you are not a key holder, you can only work during salon hours. You have a better opportunity to retail because you can have more proucts on display. And you can fit more clients in in one day because you haven't got the travelling time like when you are mobile. If you rent somewhere, you need to make sure you get a contract drawn up which states your rent and how often they are allowed to change it, whether you have to pay rent when you're on holiday, and what happens if you don't make enough money to cover rent.
hth's a little xx