website design do not complete as one-time cost. There are many website designers and companies and doing a website design once, does not end the project. There may be a need later for software to function or some third party plugins. A designer offers maintenance services or you must learn to maintain.
There is a need for the web designer to know at a minimum how one should offer mock-ups in the photoshop or on the illustrator, AI format. You may receive your logos editable version such as AI, PSD, PDF or EPS. It is up to you to decide the required.