When you are looking for a new website, you need to ensue that it has a content management system that you can use. A content management system allows users to log in and make changes to the website without having to go in to the code via FTP access. There are various content management systems out there such as off the shelf ones like WordPress and Joomla and also bespoke ones that have been built by web design companies for use with their clients only.
Often content management systems can be set up to allow different users access to different elements that they can change. For example, you may want someone to only be allowed to make text changes where as other users ay be able to delete and add new pages and make changes to the main navigation.
Most website are now built with a content management system built in but if you may be able to get a cheaper site by not having one. This is not a good idea as it will mean any change you want will have to go through the website company that built it for you and they are likely to need to charge for these changes.