There's a couple things to take into consideration. Do you want to host the software yourself? If not, look into ticketing solutions like EventBrite or similar.

If you're willing to host it, there's a ton of really good solutions available as plugins for WordPress. I work for Modern Tribe, and we make one called Events Calendar Pro which you could use with EDDTickets or WooTickets to easily make this type of website very, very quickly and easily.