This is a great question and I am in the process of working that out as well. 

So far I see there are a couple different status levels you can have and self employed is the basic one. 

I know there is the a couple clear requirements -

1. at least 3 clients

2. ability to show that your income level will be a sustainable situation

3. some kind of business plan 

4. a Fiducier

You have to show at least these things to the AVS, after that there is a need to register with your local township as a business. 

As far as advantages and disadvantages - I know that there are some tax reasons to be one of the status over the other - self employed vs. Sarl lets say but you probably should talk to a fiducier. 

The Sarl costs 5000 in fees and you have to show 20,000 in a bank account. The others are S.A. SME and there are probably a few others. 

Good luck and if you are successful please share you process. I will try to do the same. 

.... I saw you need at least three clients before you establish yourself wth the AVS, so my question is how do you bill the first three clients?  Can you just invoice as normal, but as a private individual?

I think you can initially establish them with statements of work before you actually invoice.   That being said I really do not know but most tax people will know and you have to choose a tax professional to work with you. 

I let you know next week everything I needed. I have an appointment with AVS on Tuesday. 

Why don't you join the Geneva Self Employed Professionals group of glocals?