Or will you just end up with a functioning website? What is the point of this question? What does "functioning" mean? Isn't the creation of a website simply a technical service? Depending.
Here is a question you need to ask yourself before choosing an internet agency or a web design agency, in plain English:
Would you like someone to set up a technically flawless website for you, to whom you can tell what you have in mind in every respect?
Or would you like to work with a service provider who thinks for you like an entrepreneur and designs your success, for whom technical functionality is a matter of course anyway?
Good conception is based on many factors, but the visitor to the site is always at the centre. You can only create a website that's successful with both users and search engines if your service provider understands you, understands your business model, understands your potential customers and acts accordingly.
This is the difference between user experience design and an aimlessly clicked-together website that is also somehow "pretty".