You know something, it really depends on what they are offering you and what opportunities you will gain from them.
Is this salon a really busy salon with a high demand for beauty services? Are there 4+ hair staff busy working on clients all day = if just 25% of each stylist's clients came to you for beauty services, you would be 100% booked full time immediately. It would take you years to achieve that on your own.
Or is the salon owner struggling to make business work for themselves and thinks that having a "beauty girl" will add to the takings or generate an extra £100 per week revenue? This wouldn't be a good move on your part as you would have very few beauty clients available from their existing clientele, and the salon owner might be relying on you to increase their takings magically for them.
Rather than think about rent vs. commission, why not think about potential earnings in each scenario? All that matters is you coming away with a sustainable income after X hours of work and an income that can continue to grow.
For example, I would never dream of "renting a station" for £100 a week in my salon to a beauty girl. I could put a mirror there instead and take £1,300.
The arrangement has to work for both of you mutally otherwise you'll end up 3 months down the line with the owner trying to provide as little as possible to you in return for your "flat fee rent". What other incentive do they have? See what I mean?
Alternatively, you could agree a flat rate weekly rent as suggested by some of the others, and then do a Groupon (who make you discount your prices by 70% and then take 50% of whatever you make) to get yourself some new clients.