So I'll start by saying I'm a C# .Net/Javascript developer with a lot of experience, but I have zero experience with Salesforce. Never ever seen it before today. So, I've been asked by another team to add a custom button to a Contact object, which when clicked calls an external API and updates a custom field in the Contact with the response. It was pitched as "just write some Javascript that calls an API when a button is clicked, it's literally embedded into the page, 15 minute job...".
Following what appears to be quite an outdated document, I've ended up in the Object Manager, selected the Contact object and I'm into the Buttons, Links and Actions page. I'm assuming before this was done using the Execute Javascript behaviour, which in the Lightning version I'm advised against using. So after much Googling I've read about APEX classes, Visualforce Components, Lightning Components, the Salesforce REST API, etc, etc. Not a 15 min job.
Essentially the requirements are to embed a button (or action, or..?) into this Contact page, so that when the sales guy clicks it, it gathers some of the Contact's details and uses them to form an API call to an external service. The data will be used to form a response, which must then be read (as JSON, then parsed) and written into a custom field on the Contact.
What would be the best approach for developing a solution? In the Apex Debug environment I've put together the code to call the API and parse the JSON response, I'm assuming I need to wrap this in an Apex class, with a method that calls this code and returns the response. What I'm not sure of is how to call into this from the button, and update the field in the Contact. Do I need to do all that from the Apex Class method? passing in a reference to the Contact, or is there another component that needs to sit in between and do this. Am I right in assuming I'll need to use the Salesforce API to update the Contact?
Any pointers appreciated.

