The essentials would be:

* 7231 which covers core methods, statuses and basic headers. It looks like the spec authors have also added security considerations sections

* 7232 is probably a good read as it covers conditional requests (304 and 412 statuses)

* 7234 covers caching and cache controls, don't skip it. Even if you don't want your response to be cached, you need to know how caching works, which actors are involved and how to disable it

* 7238 is the 308 redirection, understanding it and the background for its introduction is a good idea and will help with understanding other redirection statuses (301, 302 and 307)

"Various others" would be

* 7233 is Range requests, can probably be skipped unless you have big media payloads. On one hand it's underused, on the other hand it has limited general applicability

* 7235 is Authentication, can be useful for API (the user experience being terrible for browsers) but can probably be skipped unless absolutely necessary

* 7239 is forwarding, to understand what happens when your HTTP endpoint is behind a proxy. Although I'd guess proxies don't implement it yet the ideas already existed as non-standard extensions and reading this is a good idea for "real-world" concerns. Not completely necessary, but useful

* 7240 is the Prefer header. It's a fairly recent and quite advanced addition, probably useful but not utterly necessary

You can ignore

* 7230 is about req/resp format. The only interesting parts are the URI and Host parts which your HTTP library probably handles for you

* 7236 complements 7235 with auth scheme registration for standard auth types. Only read it if you've read 7235

* 7237 is a registry of additional (wrt 7231) methods, mostly from WebDAV