Maybe the utmost important is that you will pay the right price! For example: a website made with a program, which are HTML pages should cost between 100 and 300 dollars, where a CMS website made with Joomla can cost between 300 and 1500 dollars depending on the amount of pages, the use of a shopping cart system and payment options like credit cards. Also you want to have a website made without any recurring costs. If for example they use a private CMS system and want to charge you a monthly 20 dollars for that, you will pay around 2400 dollars over the next ten years. Would they use for example Wordpress there would be no costs over the next ten years except for hosting your website.
You are about to have a website made by a professional webdesigner? Then you should certainly watch out which company you hire for the job, as not all webdesigners that offer their services to you are professional people. Unemployed persons often just start a business of making websites because nowadays it is an easy thing to do. All sorts of CMS systems aren't very hard to learn like Joomla and Drupal, also there are a lot of programs on the market that create in no-time HTML websites. This means that someone that has never studied anything concerning webdesign can easily fool you and pretend to have a lot of knowledge without this being the truth. You understand this is not the people you targeted for to have a website made! Therefore always ask them where they have studied and have a look at their so called portfolio, websites the have constructed for previous clients.