You probably need a couple plugins to do this. I use Woocommerce for just about everything – there is a ton of plugins and a lot of support online.
Get Woocommerce for free through the wordpress repository. Set up your store through there. Then you will need Woocommerce subscription & Woocommerce Membership – it is the best to use for something like this.
Get a free membership over at gpldl.com – a great site where you can download these woocmmerce plugins for free once you are signed up. Once signed up – go to https://gpldl.com/repository/premium-woocommerce-extensions/ and get “WooThemes Subscriptions WooCommerce Extension” and install it. Finally – you will want “WooCommerce – Memberships WooCommerce Extension” which can also be downloaded at gpldl.com.
Once you have these plugins – you should be able to follow the setup instructions and get your membership site up and running.