WordPress updates can be a daunting thing to new users. Fear not, WordPress has one of the easiest updating systems around, and the core is designed to be as backwards compatible as possible.
When you have some updates to do, always update core first, then update your plugins and themes right after.
After an update, you should always check that the site is working as expected. If there are any issues, you can contact the support staff of the plugin or theme you are using. Contacting support when your core is not yet updated is fruitless because good developers always test on the latest version of WordPress, and will mostly ask you to get your site up to the latest version as well to help in trouble shooting.
So there you have it, an answer to a question that gets asked often around here.