First of all I would suggest wordpress, its not perfect but its pretty good.
You can turn of branding in the settings in the admin area. There is no "premium wordpress".
A CMS like WIX, SQUARESPACE etc. will all charge a monthly fee.
There are plenty of free themes around or marketplace such as Themeforest that you can buy some amazing templates.
Wordpress is extremely customisable, and can vary from theme to theme. Each layout is different, some are super customisable, even some that are specialty designs for full customisation.