In my opinion, any web site designer worth their salt would start out by asking what you want; if you are in need of ideas, then good places to start are by looking at your existing marketing material (e.g. business cards, flyers, price list brochures etc), as it is a good idea to go for a web site that reinforces your existing brand identity, as this will help you build a strong brand across all media (which will help people remember your salon better, e.g. if they see your website, and then an advert in the local paper with the same graphic design and colours).
If there are already web sites that you like the look of (perhaps in terms of layout or navigation), and you already have existing printed marketing material, then it would be a good idea to suggest that your web designer tries to integrate the "look" of your existing material in with a similar layout/navigation to the web site that you like. But it's never a good idea to blatantly rip off the design of someone else's site!
If you're starting out, and don't have a brand identity/logo/printed material, then it would make sense to speak to someone who has both strong graphic design and web design skills. As that way, you would be guaranteed a strong brand identity across all media from the start. A good starting point being a logo and colour scheme.
The primary difference between most "static" websites (which just display plain HTML content that doesn't change unless someone uploads new HTML files or images etc) and sites which offer an online shop, etc, is that a lot of additional technology is required on the web server to manage the online shop.
Most "static" web sites will be served up by a web server such as Apache, or Microsoft IIS (Internet Information Services); an online shop will require a database to store details of products, stock levels, customer details, orders, etc, and associated code to "power" the interactive features of the website, usually written in a language such as Java, PHP or Microsoft .NET - this will require a lot more work on the part of the web designer and they will likely also need additional software engineering skills - hence such sites are generally a fair bit more expensive. Some companies do offer "off the shelf" e-commerce solutions, however, but you would need to be sure that they would meet your requirements before committing yourself.
Then you would need to consider issues such as security and data protection legislation; I would consider it a necessity for payment details (e.g. credit card numbers etc) to be sent over secure HTTP (HTTPS/SSL), for example (as this encrypts the data so that it can't be "intercepted" in its journey across the internet between the customer's web browser and the online shop's server); it's almost certainly good practice to use HTTPS for customer name and address details too. Then there is the need to register with the Information Commissioner's Office (ICO) if storing details of individuals on a computer system that could be used to uniquely identify them. However, a reputable company should be aware of such requirements and advise you accordingly.
In terms of whether a web site generates you any clients - well a good starting point would be to make use of web statistics software, such as Webalizer (which is an open source [i.e. free] web statistics analyser that I know works very well with Linux and Apache - but would require the web host to install and configure), and Google Analytics (which works by adding a snippet of code to your web pages, and transmits data to Google every time someone visits your web site, and then you log on to Google to view your web traffic - but be aware of the privacy implications of Google storing this information). Both these systems will give you details of how many people visit your site each day, which links they click on to get there (e.g. a Google search result, an advert on Gumtree, etc), and (using something called Geo IP location), a rough guide as to which country they are visiting from. If you find that the number of new clients increases with the number of hits to your site, then you'll be able to place a fair bet that your site is working to bring you in new clients.
Of course there are other things that could help with that too, e.g. having a "contact form" on your site, where prospective clients can email you to find out more about your services, and (better still) an email list facility, where people can sign up and will then receive periodical email messages from you, perhaps giving details of new treatments/products, and special offers, etc. Another thing you could consider is a "testimonials" page, where happy clients can leave feedback about your services.
