Most of the free hosts provide you an Admin Panel, like CPanel or Vista Panel. There is an option to make the databases, add and modify Cron jobs etc.
Website Builders are often so limited that you can't make a game with them. They are for people who have little to no experience of HTML, and if you have none you can pretty much forget the game-making until you know it. You also need to learn some server side language like PHP or ASP and learn to use database like MySQL. Learning them might take some time, but don't be discouraged, the basics are easy to learn.
Go to
Tizag and read trough their tutorials, they are a great starting point and have all the information how to make a game.
