Game websites rely on two major aspects on the web. They rely heavily on website layout, and website functionality. Developing the website is the major portion and will generally take some programming to create the functionality. There are several third party tools you can use to assist you, which is where most beginners begin. There are also tons of different type of CMS(Content Management Systems) you can use, which also requires some learning. When it comes to hosting I believe the best system might just entail something like a cpanel hosting plan, that provides php and a CMS with it Wordpress is well known has quite a community, that may be your best bet.